MATH SOLVE

4 months ago

Q:
# Match each exponential function to its percent rate of change.

Accepted Solution

A:

This question is about exponent function. All the function in this question is following a pattern of f(x)= a[tex] (b)^{x} [/tex]In this function, a is the initial/starting quantity and b is the base of the exponent. The option in this problem is about growth/decay that was determined by the base of the exponent. So, to answer this question you just need to pay attention to the variable b

1. Answer: 4% grow

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 46(1.04)²

Then the value of the variable would be:

a= 46

b=1.04

Since b is >1 then it is a growing function. The grow in percent would be: (1.04 * 100%) - 100%= 104%-100%=4%

2. Answer: 4% decay

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 104(0.96)²

Then the value of the variable would be:

a= 104

b=0.96

Since b is <1 then the function would decay. The rate of change percent would be: (.96 * 100%) - 100%= 96%-100%= -4%. The function rate of change is 4% decay

3. Answer: 40% decay

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 74(0.6)²

Then the value of the variable would be:

a= 74

b=0.60

Since b is <1 then the function would decay. The rate of change percent would be: (0.60 * 100%) - 100%= 60%-100%= -40%. The function rate of change is 40% decay

4. Answer: growth 40%

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 44(1.4)²

Then the value of the variable would be:

a= 44

b=1.4

Since b is >1 then the function would grow. The rate of change percent would be: (1.40 * 100%) - 100%= 140%-100%= 40%. The function rate of change is 40% growth

5. Answer: 14% decay

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 40(0.86)²

Then the value of the variable would be:

a= 40

b=0.86

Since b is <1 then the function would decay. The rate of change percent would be: (0.86 * 100%) - 100%= 86%-100%= -14%. The function rate of change is 14% decay

6. Answer: 14% growth

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 8(1.14)²

Then the value of the variable would be:

a= 8

b=1.14

Since b is >1 then the function would grow. The rate of change percent would be: (1.14 * 100%) - 100%= 114%-100%= 14%. The function rate of change is 14% growth

1. Answer: 4% grow

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 46(1.04)²

Then the value of the variable would be:

a= 46

b=1.04

Since b is >1 then it is a growing function. The grow in percent would be: (1.04 * 100%) - 100%= 104%-100%=4%

2. Answer: 4% decay

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 104(0.96)²

Then the value of the variable would be:

a= 104

b=0.96

Since b is <1 then the function would decay. The rate of change percent would be: (.96 * 100%) - 100%= 96%-100%= -4%. The function rate of change is 4% decay

3. Answer: 40% decay

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 74(0.6)²

Then the value of the variable would be:

a= 74

b=0.60

Since b is <1 then the function would decay. The rate of change percent would be: (0.60 * 100%) - 100%= 60%-100%= -40%. The function rate of change is 40% decay

4. Answer: growth 40%

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 44(1.4)²

Then the value of the variable would be:

a= 44

b=1.4

Since b is >1 then the function would grow. The rate of change percent would be: (1.40 * 100%) - 100%= 140%-100%= 40%. The function rate of change is 40% growth

5. Answer: 14% decay

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 40(0.86)²

Then the value of the variable would be:

a= 40

b=0.86

Since b is <1 then the function would decay. The rate of change percent would be: (0.86 * 100%) - 100%= 86%-100%= -14%. The function rate of change is 14% decay

6. Answer: 14% growth

f(x)= a[tex] (b)^{x} [/tex]

f(x)= 8(1.14)²

Then the value of the variable would be:

a= 8

b=1.14

Since b is >1 then the function would grow. The rate of change percent would be: (1.14 * 100%) - 100%= 114%-100%= 14%. The function rate of change is 14% growth