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