Question

Match each exponential function to its percent rate of change.

Answer 1

This question is about exponent function. All the function in this question is following a pattern of f(x)= a$(b)^{x}$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$(b)^{x}$
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$(b)^{x}$
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$(b)^{x}$
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$(b)^{x}$
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$(b)^{x}$
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$(b)^{x}$
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