35 years
Step-by-step explanation:
Given that:
Current deer population, P0 = 800
Growth rate = 20% yearly
For the population to double in size, P = 2 * P0 = 2 * 800 = 1600
t = number of years
Using the relation :
P =P0(1 + r)^t
1600 = 800(1 + 0.2)^t
1600 / 800 = (1.02)^t
2 = (1.02)^t
t = log2 / log(1.02)
t = (0.3010299 / 0.0086001)
t = 35.003069
t = 35 years