The growth factor of g is given by [tex]A = e^{0.6t}.[/tex]
The function exhibits exponential growth.
We have,
(a)
Let's denote the growth factor as A(t), where t is the independent variable representing time.
The rate of change of g at any time t is proportional to g itself, with a constant of proportionality of 0.6.
This can be expressed as:
dA/dt = 0.6A
This is a separable differential equation, which we can solve by separating the variables and integrating them:
1/A dA = 0.6 dt
Integrating both sides,
ln|A| = 0.6t + C
Here, C is the constant of integration.
Exponentiating both sides:
[tex]|A| = e^{0.6t + C}[/tex]
Since the growth factor A is always positive, we can drop the absolute value:
[tex]A = e^{0.6t + C}[/tex]
We can do this by considering the initial condition.
Let's assume that at t = 0, the growth factor A is 1 (no growth). Substituting these values into the equation:
[tex]1 = e^{0.6(0) + C}\\1 = e^C[/tex]
Taking the natural logarithm of both sides:
[tex]ln(1) = ln{e^C}[/tex]
0 = C
So,
[tex]A = e^{0.6t}[/tex]
(b)
The function g exhibits exponential growth, as the value of g increases exponentially with time.
Thus,
The growth factor of g is given by [tex]A = e^{0.6t}.[/tex]
The function exhibits exponential growth.
Learn mroe about exponential functions here:
https://brainly.com/question/33520267
#SPJ4
The growth factor of gg is 0.6. The function exhibits exponential growth.
Explanation:(a) The growth factor of an exponential function is the base of the exponent. In this case, the growth factor is 0.6.
(b) The function gg exhibits exponential growth, meaning that as the input increases, the output increases at a proportional rate.
Learn more about Exponential growth here:https://brainly.com/question/12490064
#SPJ12
Solve for y 3x-4y=10
The product of two consecutive even integers is 80. find all such pairs of integers
The possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -
(8, 10)
(- 10, - 8)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given product of two consecutive even integers is 80.
Assume that the first integer is [n]. Then the second integer will be [n + 2]. According to the question, we can write -
n x (n + 2) = 80
n² + 2n = 80
n² + 2n - 80 = 0
n² + 10n - 8n - 80 = 0
n(n + 10) - 8(n + 10)
(n - 8)(n + 10) = 0
n = 8 and n = - 10
If → n = 8 then (n + 2) = 10.
If → n = - 10 then (n + 2) = -8.
Therefore, the possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -
(8, 10)
(- 10, - 8)
To solve more questions on equation modelling, visit the link below-
https://brainly.com/question/17965009
#SPJ5
Final answer:
The consecutive even integers whose product is 80 are 8 and 10. This is found by setting up an equation for consecutive even integers and factoring the number 80.
Explanation:
The question is asking to find two consecutive even integers whose product is 80. When two numbers are consecutive even integers, they can be represented as n and n + 2, where n is an even integer. To find these numbers, we set up the equation n(n + 2) = 80.
First, we need to find two numbers that multiply to give 80. We can start by listing the factors of 80: 1 x 80, 2 x 40, 4 x 20, 5 x 16, 8 x 10. Since we are looking for even integers, we pick the pairs where both numbers are even: 4 x 20, 8 x 10. However, the numbers must also be consecutive even integers, which is the case for the pair 8 and 10, but not for 4 and 20.
Therefore, the pair of consecutive even integers that multiply to give 80 are 8 and 10.
Two months ago, the mean daily rainfall in a local city was 9.4 cm. The mean absolute deviation was 3.5 cm. Last month, the mean daily rainfall in that city was 11.5 cm, and the mean absolute deviation was 1.6 cm.
Which statement about the rainfall is true?
More rain fell two months ago than last month.
About the same amount of rain fell two months ago as last month.
Last month, the amount of rain that fell each day varied about the same as the month before.
Last month, the amount of rain that fell each day varied less than the month before.
Answer:
C
Step-by-step explanation:
Last month, more rain fell compared to two months ago, and there was less variation in the daily rainfall.
Explanation:To determine whether more rain fell two months ago or last month, we need to compare the mean daily rainfall and the mean absolute deviation for both months. Two months ago, the mean daily rainfall was 9.4 cm with a mean absolute deviation of 3.5 cm. Last month, the mean daily rainfall was 11.5 cm with a mean absolute deviation of 1.6 cm.
Thus, based on this information, we can conclude that more rain fell last month. The mean daily rainfall was higher and the mean absolute deviation was lower. This indicates that there was less variation in the amount of rain that fell each day last month compared to two months ago.
Colby worked three more hours on tuesday than he did on monday. on wednesday, he worked one hour more than twice the number of hours that he worked on monday. if the total number of hours is two more than five times the number of hours worked on monday, how many hours did he work on monday>
Answer:
a,b,c
Step-by-step explanation:
i guessed and then they told me the right answer .
Identify the values of a b and c in the quadratic function y = 3x -5x +2
This year, the parade had 127 floats. That was 34 fewer floats than last year. How many floats were in te parade last year ?
Answer:
Last year were 161 floats, that is, 34 more than this year.Step-by-step explanation:
Givens
There are 127 floats this year.That represents 34 fewer floats than last year.The second given statement expresses that this year there are 34 LESS floats. So, to know how many floats were there last year, we just need to sum
[tex]127+34=161[/tex]
Therefore, last year were 161 floats, that is, 34 more than this year.
What is the mixed number for -10.125
Write in simplest form please!
Diameters AB and CD of circle K intersect such that m∠BKD = 100°. The measure of arc AC is:
Answer:
Measure of arc AC = 100°
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
Given : AB and CD are the diameters of the circle K and m∠BKD = 100°
To find : measure of arc AC
Solution :
The angle which is formed by the arc AC is m∠AKC so we need to find the measure of the angle ∠AKC
Now, m∠BKD = 100°
and m∠BKD = m∠AKC ( Vertically opposite angles are always equal)
⇒ m∠AKC = 100°
Hence, Measure of the arc AC = 100°
What has a greater area, a square or an equilateral triangle?
What is the playing surface called where the college basketball semi- finals are played
The playing surface where the college basketball semi-finals are played is called the court. It is rectangular in shape and has various markings such as the three-point line and free-throw line.
Explanation:The playing surface where the college basketball semi-finals are played is called the court or the basketball court. The court is rectangular in shape with a length of 94 feet and a width of 50 feet. It is divided into two halves with a midcourt line and has markings such as the three-point line, free-throw line, and key.
Learn more about Basketball court here:https://brainly.com/question/27824350
#SPJ2
what is 5 divided by 9374
Determine the exponential function that satisfies the given conditions:
The initial mass is 1.4g and it is halving every 4 days.
To determine the exponential function, use the general form of an exponential function and substitute the given values. The equation is y = 1.4 * (1/2)^(x/4).
Explanation:An exponential function represents exponential growth or decay. In this case, the given information states that the initial mass is 1.4g, and it is halving every 4 days. We can use the general form of an exponential function, y = ab^x, where a is the initial value, b is the growth/decay factor, and x is the time in days.
Since the mass is halving every 4 days, the decay factor is 1/2, since the mass is halving. The equation becomes y = 1.4 * (1/2)^(x/4).
This equation represents the exponential function that satisfies the given conditions.
Gina bought 2.3 pounds of red apples and 2.42 ponds of green apples. They were on sale for 0.75 a pound. How much did the apples cost altogether?
Find y'' by implicit differentiation .4x3 + 5y3 = 9
y'' by implicit differentiation is y'' = -16x/5y^3.
To find y'' by implicit differentiation, we need to differentiate both sides of the equation .4x3 + 5y3 = 9 twice with respect to x.
First, we differentiate both sides once with respect to x to find dy/dx. This gives us:
12x^2 + 15y^2 (dy/dx) = 0
Next, we differentiate both sides once again with respect to x to find d^2y/dx^2 (y''). This gives us:
24x + 30y^2 (dy/dx) + 15y^2 (d^2y/dx^2) = 0
We can now solve for d^2y/dx^2 (y'') by substituting dy/dx from the first equation into the second equation. This gives us:
24x + 30y^2 (-12x^2/15y^2) + 15y^2 (d^2y/dx^2) = 0
Simplifying this equation, we get:
d^2y/dx^2 = -16x/5y^3
Therefore, y'' = -16x/5y^3.
for such more question on implicit differentiation
https://brainly.com/question/11887805
#SPJ3
I WILL MARK BRAINLIEST ANSWER
What is the equation of the following graph in vertex form?
y = (x − 3)2 − 1
y = (x + 3)2 − 1
y = (x − 4)2 − 2
y = (x − 4)2 + 8
Answer:
y = (x + 3)2 − 1
:)
A baker sells bread for $5 a loaf and rolls for $1 each. The baker needs to sell $35 worth of baked goods by the end of the day. Enter a linear equation that describes the problem.
Explanation:
Cost of 1 loaf of bread = $5
Cost of 1 roll = $1
The baker needs to sell both items and it should be worth $35.
To find the linear equation, Suppose, the baker sells “b” loaves of bread and “r” rolls.
Then the total cost of the sales has to be $35.
So, the linear equation will be:
5b + 1r = 35
What is the solution of the system? Use the elimination method. 2x+y=206x−5y=12 Enter your answer in the boxes.
Answer:
The answer to your question is: x = 7; y = 6
Step-by-step explanation:
2x+y=20 ( 1 ) Multiply by 5
6x−5y=12 ( 2 )
5 (2x+y=20) = 10x + 5y = 100
10x + 5y = 100
6x − 5y = 12 Eliminate y
16 x = 112
x = 112 / 16
x = 7
2(7) + y = 20 Substitution
14 + y = 20
y = 20 - 14
y = 6
Which proportion could be used to solve the question?
What percent of 80 is 23?
A. p/23 = 80/100
B. p/80 = 23/100
C. p/100 = 23/80
D. none could be used
what is the common ration between successive term in the sequance? 2,-4,8,-16,32,-64
PLEASE HELP!!!!!!!!!
solve for x
-2(x+1/3)+9x=4
x=
A 3-cup bottle of dish soap costs $5.28. What is the price per fluid ounce?
Answer:A 3-cup bottle of dish soap costs $3.36. What is the price per fluid ounce.
Step-by-step explanation:
4/3 of a number is 20. What is the number?
What are the odd numbers between 3497 and 3511?
A conjecture and the paragraph proof used to prove the conjecture are shown.
Drag an expression or statement to each box to complete the proof.
It is given that ∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank]
choices:
verticle angle theorim, transitive property of congruence, ∠4, ∠3, ∠2, ∠1
Answer:
∠2; vertical angle theorem; ∠3; transitive property of congruence
Step-by-step explanation:
∠2 and ∠1 are opposite angles that share only a vertex. This is the definition of vertical angles, and by the vertical angle theorem they are congruent.
Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.
∠4 and ∠3 are opposite angles that share a vertex. This makes them vertical angles, and the vertical angle theorem states that they are congruent.
The transitive property, algebraically, states "if a=b and b=c, then a=c." Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."
The required solution for the blacks,
Blank 1 = ∠2;
Blank 2 = vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.
It is given that
∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank].
To determine the missing statement at the place of blanks in the statement.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Since
Black 1
∠2≅∠4
and ∠1≅ ∠4
So ∠2 ≅ ∠1
Blank 2
∠2≅∠4 are equal by the vertical angle theorem.
Blank 3
∠4≅∠3
∠3 ≅∠1
So,
∠2 ≅ ∠1 ; ∠2≅∠3 and ∠4≅∠3 it is transitive property of congruence.
Thus, the required solution for the blacks,
Blank 1 = ∠2;
Blank 2 = vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ2
Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session.if Allison already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal ?
write an equation for the line that passes through (2,-5) and is parallel to 3x+4y=8
The equation of the line which is parallel to the line 3x+4y=8 and passes through the point (2,-5) is y = -3/4x - 1/2.
Explanation:The given equation is 3x+4y=8, which is a linear equation. To make this simpler, we can isolate 'y' to make it in the form 'y = mx + b', where 'm' is the slope. When we do this, we get y = -3/4x + 2, so the slope of this line is -3/4.
Next, we know that parallel lines have the same slope. Therefore, the equation of the line parallel to the given line and passing through (2, -5) will also have a slope of -3/4. Using the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line, and 'm' is the slope, we can substitute the given values.
Therefore, y - (-5) = -3/4(x - 2), simplifying this gives us the equation of our line: y = -3/4x - 1/2.
Learn more about Equation of linehttps://brainly.com/question/7150168
At a discount grocery store, Jessica paid 0.72 for an 8-ounce bottle of spring water. What is the cost of the spring water per ounce?
The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) = x²?
I’ll mark brainliest!!!!!! Please help me someone, anyone
What is the value of x ?
Maths question below please help