Question

ential growth functions
what is the rate of change of the function described in the table?
5
$\frac{12}{5}$
25
$\frac{25}{2}$

$x$	$y$
0	$\frac{1}{5}$
1	1
2	5
3	25

Explanation:

Step1: Identify exponential form

The table follows $y = ar^x$, where $r$ is the growth rate.

Step2: Use x=0 to find a

When $x=0$, $y=\frac{1}{5}$, so $a=\frac{1}{5}$.

Step3: Solve for r with x=1

Substitute $x=1, y=\frac{1}{2}$:
$\frac{1}{2} = \frac{1}{5}r^1$
$r = \frac{1}{2} \div \frac{1}{5} = \frac{5}{2} \times 1 = 5$
Verify with $x=2$: $\frac{1}{5} \times 5^2 = \frac{25}{5}=5$, which matches the table.

Answer:

5