Question

The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?

F.2084
G.2044
H.2043
J.2085

Answer 1

9514 1404 393

Answer:

J. 2085

Explanation:

Fill in the desired value for y and solve for x.

1500 = 50(1.05^x)

30 = 1.05^x . . . . . . . divide by 50

log(30) = x·log(1.05) . . . . . take logarithms

x = log(30)/log(1.05) ≈ 69.71

Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.