Question

The deer population of a certain area is modeled by the formula: P=578e^0.045t where t is measured in years. In approximately how many years will the deer population reach 3000? 37.4 years 34.7 years 35.8 years 36.6 years

Answer 1

36.6 years

Explanation:

Here, we are to find the number of years it will take for the population of deers to reach 3,000

What to do here is simply substitute the value of 3,000 for P and use it to find t

3000 = 578e^0.045t

Divide through by 578

5.1903 = e^0.045t

Take the ln (natural logarithm of both sides)

Recall ln e = 1

ln 5.1903 = ln e^0.045t

ln 5.1903 = 0.045t

0.045t = 1.6468

t = 1.6468/0.045

t = 36.595 years which is 36.6 years