Find an exponential model for the following data set.

A) $y = 36.07 \times 1.25 ^ { t }$
B) $y = 0.8 \times 36.07 ^ { t}$
C) $y = 36.07 \times 0.8 ^ { t}$
D) $y = 1.25 \times 36.07 ^ { t}$

Question

Find an exponential model for the following data set.

A) $y = 36.07 \times 1.25 ^ { t }$ 
B) $y = 0.8 \times 36.07 ^ { t}$ 
C) $y = 36.07 \times 0.8 ^ { t}$ 
D) $y = 1.25 \times 36.07 ^ { t}$

Quizplus · Accepted Answer

An exponential model has the form y = ab^t, where a is the initial value and b is the growth factor. Looking at the data set, we can see that the population is decreasing over time, so we need a growth factor less than 1. Option C has a growth factor of 0.8, which fits this requirement. Additionally, the initial value of the population can be approximated at around y = 60, which is closest to the value given in option C (36.07). Therefore, option C is the best choice for an exponential model of the given data set.

Find an Exponential Model for the Following Data Set y=36.07×1.25ty = 36.07 \times 1.25 ^ { t }y=36.07×1.25t

Find an Exponential Model for the Following Data Set $y = 36.07 \times 1.25 ^ { t }$