Question

x | y
-1 | 1/10
0 | 1/2
1 | 6/2
2 | 30/2
3 | 125/2
what is the rate of change of the function described in the table?
options: 11/5, 5, 15/2, 25

Explanation:

Step1: Identify function type

Check if it's linear (constant Δy/Δx) or exponential (constant ratio of y-values).

Step2: Calculate y-value ratios

$\frac{\frac{1}{2}}{\frac{1}{10}} = 5$, $\frac{\frac{6}{2}}{\frac{1}{2}} = 6$ (wait, correction: $\frac{\frac{5}{2}}{\frac{1}{2}} = 5$; $\frac{\frac{25}{2}}{\frac{5}{2}} = 5$; $\frac{\frac{125}{2}}{\frac{25}{2}} = 5$)

Step3: Confirm exponential growth rate

For exponential functions $y = ab^x$, the growth factor $b=5$, which is the multiplicative rate of change.

Answer:

5