Answer:
47 years
Step-by-step explanation:
The population decay can be modeled by an exponential function of the form ...
p = a·b^t
where a is the initial population, and b is the growth factor.
__
The growth factor is related to the given growth rate by ...
growth factor = 1 + growth rate
b = 1 + (-3.5%) = 1 -0.035 = 0.965
The initial population is given as a=80, so the exponential function is ...
p = 80·0.965^t
__
We want to find the value of t when p=15. This is solved using logarithms.
15 = 80·0.965^t
15/80 = 0.965^t . . . . . . . . . . . divide by 80
log(15/80) = t·log(0.965) . . . . take logs
t = log(15/80)/log(0.965) ≈ 46.985 . . . . divide by the coefficient of t
After 47 years, the population will drop below 15 lions.
