Answer:
a) 500
b) 9.6 years
Step-by-step explanation:
Population of Ilamas
a) P = 500 e ^0.035t
Find P when t = 0
Solving for P
P = 500 e ^0.035 × 0
P = 500 × e ⁰
P = 500 × 1
P = 500
The population of the Ilamas when t = 0 is 500
b ) Find t when P = 700
P = 500 e ^0.035t
700 = 500 e ^0.035t
Divide both sides by 500
700/500 = 500 e ^0.035t/500
7/5 = e ^0.035t
1.4 = e ^0.035t
Take In of both sides
In 1.4 = In (e ^0.035t)
In 1.4 = 0.035t
t = In 1.4/0.035
t = 0.3364722366/0.035
t = 9.6134924749 years
t = Approximately to the nearest tenth of a year = 9.6 years
