a small business invested its profits into an account. the table provides data for the account balance, in dollars, over several years of the account life. what is the exponential regression equation that models the dataset.

Question

a small business invested its profits into an account. the table provides data for the account balance, in dollars, over several years of the account life. what is the exponential regression equation that models the dataset. 
year: 0.5, 1, 2, 2.5, 3
account value$: 560, 1035, 3495, 6548, 9859
a. y=321.67(3.22)^X
b. y=321.67(3.23)^X
c. y=3.22(321.67)^x
d. y=3.23(321.67)^x

GPT-4o mini · Answer

To find the exponential regression equation that models the dataset, we need to conduct an exponential regression analysis on the provided data points.

The given data points are:

Year (x): 0.5, 1, 2, 2.5, 3
Account value $y$: 560, 1035, 3495, 6548, 9859

To perform an exponential regression, we'll typically use the form:

\[ y = a \cdot b^x \]

where $a$ is the value when $x = 0$ and $b$ is the growth factor.

Using software or a calculator that has regression capabilities (or through manual calculation), you can typically compute the best-fit coefficients $a$ and $b$.

For this particular dataset, after performing the calculation, we can determine that the best-fit model is:

\[ y \approx 321.67 \cdot (3.23)^x \]

Based on the provided options, the correct answer is:

b. $y = 321.67(3.23)^x$