Question

land the average price of 1 acre of land in berrien county is currently $7152 and is increasing at an annual rate of 2.1%. which function represents the estimated average price of 1 acre of land in berrien county after $x$ years?
a) $y = 7152(0.021)^x$
b) $y = 7152(0.21)^x$
c) $y = 7152(1.021)^x$
d) $y = 7152(2.1)^x$

Explanation:

Step1: Recall growth function form

The general exponential growth formula is $y = a(1+r)^x$, where $a$ is the initial value, $r$ is the annual growth rate (in decimal), and $x$ is time in years.

Step2: Convert rate to decimal

Convert 2.1% to decimal: $r = \frac{2.1}{100} = 0.021$

Step3: Substitute values into formula

Initial value $a=7152$, so the function is $y = 7152(1+0.021)^x = 7152(1.021)^x$

Answer:

C) $y = 7152(1.021)^x$