Question

in the exponential function f(x) = 5·(1 + 09)^x, what is the exponential growth rate?
a. 5%
b 1%
c 9%
d 1 09%

Explanation:

Step1: Recall exponential growth formula

The general form of an exponential growth function is \( f(x) = a(1 + r)^x \), where \( a \) is the initial amount, \( r \) is the growth rate (expressed as a decimal), and \( x \) is the independent variable.

Step2: Compare with given function

Given the function \( f(x) = 5 \cdot (1 + 0.09)^x \). Comparing this with the general form \( f(x) = a(1 + r)^x \), we can see that \( 1 + r = 1.09 \).

Step3: Solve for r

To find \( r \), we subtract 1 from both sides of the equation \( 1 + r = 1.09 \). So, \( r = 1.09 - 1 = 0.09 \).

Step4: Convert to percentage

To convert the decimal \( 0.09 \) to a percentage, we multiply by 100. So, \( 0.09 \times 100 = 9\% \).

Answer:

C. 9%