To determine the multiplicative rate of change for the exponential function represented in the given table, we follow these steps:
1. Understand the Definition:
The multiplicative rate of change for an exponential function can be found by dividing consecutive y-values. It should be constant for an exponential function.
2. List the Values:
First, we list the given y-values from the table:
[tex]\[
y_1 = 4.5, \quad y_2 = 6.75, \quad y_3 = 10.125, \quad y_4 = 15.1875
\][/tex]
3. Compute the Consecutive Ratios:
To find the multiplicative rate of change, we will calculate the ratio of each y-value to its preceding y-value.
[tex]\[
\text{Ratio from } y_1 \text{ to } y_2 = \frac{y_2}{y_1} = \frac{6.75}{4.5} = 1.5
\][/tex]
[tex]\[
\text{Ratio from } y_2 \text{ to } y_3 = \frac{y_3}{y_2} = \frac{10.125}{6.75} = 1.5
\][/tex]
[tex]\[
\text{Ratio from } y_3 \text{ to } y_4 = \frac{y_4}{y_3} = \frac{15.1875}{10.125} = 1.5
\][/tex]
4. Identify the Multiplicative Rate of Change:
Since the ratios between the consecutive y-values are all the same, we confirm that the multiplicative rate of change for this exponential function is 1.5.
Thus, the correct answer is 1.5.
