Answer:
Step-by-step explanation:
We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^ t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 100
r = 24% = 24/100 = 0.24,
The exponential model for this population becomes
A = 100(1 + 0.24)^t
A = 100(1.24)^t
1) When t = 5 years,
A = 100(1.24)^5
A = 293
2) When t = 10 years,
A = 100(1.24)^10
A = 859
3) When A =1000
1000 = 100(1.24)^t
1000/100 = (1.24)^t
10 = (1.24)^t
Taking log of both sides to base 10, it becomes
Log 10 = log 1.24^t
1 = t log 1.24
1 = 0.093t
t = 1/0.093
t = 11 years to the nearest whole year.
