Find an exponential model for the following data set.

A) $y = 36.05 \times 1.67 ^ { t }$
B) $y = 0.6 \times 36.05 ^ { t }$
C) $y = 36.05 \times 0.6 ^ { t }$
D) $y = 1.67 \times 36.05 ^ { t }$

Question

Find an exponential model for the following data set.

A) $y = 36.05 \times 1.67 ^ { t }$ 
B) $y = 0.6 \times 36.05 ^ { t }$ 
C) $y = 36.05 \times 0.6 ^ { t }$ 
D) $y = 1.67 \times 36.05 ^ { t }$

Quizplus · Accepted Answer

The exponential model is of the form $y = ab^t$, where $a$ is the initial value and $b$ is the growth factor. To find $a$ and $b$, we can plug in the first data point $(0,36.05)$ and solve for $a$, and then plug in the second data point $(1,21.63)$ and solve for $b$.

Plugging in $(0,36.05)$, we get $36.05 = ab^0 = a$.

Plugging in $(1,21.63)$, we get $21.63 = ab^1 = 36.05b$. Solving for $b$, we get $b \approx 0.6$.

Thus, the exponential model is $y = 36.05 	imes 0.6^t$, which is choice $\boxed{	extbf{(C)}}$.

Find an Exponential Model for the Following Data Set y=36.05×1.67ty = 36.05 \times 1.67 ^ { t }y=36.05×1.67t

Find an Exponential Model for the Following Data Set $y = 36.05 \times 1.67 ^ { t }$