ez: Attempt 2
Question 12 (2 points)
Given the table of values, write an equation that will represent the exponential growth or decay
\begin{tabular}{|l|l|l|l|l|}
\hline 0 & 1 & 2 & 3 & 4 \\
\hline 15 & 60 & 240 & 960 & 3840 \\
\hline
\end{tabular}
Answer
The equation that represents the exponential growth is \(\boxed{y = 15 \cdot 4^x}\).
Step 1 ：Given the table of values, we are asked to write an equation that will represent the exponential growth or decay.
Step 2 ：The given table represents an exponential function. The y-values are increasing by a factor of 4 as the x-values increase by 1. This suggests that the base of the exponential function is 4.
Step 3 ：The initial value (when x=0) is 15. Therefore, the equation of the function is of the form \(y = ab^x\), where a is the initial value and b is the base of the exponential function.
Step 4 ：The equation that represents the exponential growth is \(\boxed{y = 15 \cdot 4^x}\).
