Answer:
23 years
Step-by-step explanation:
The equation for the exponential growth of the population can be written as ...
population = (initial value)×(1 + (growth rate))^t
where t is the time period applicable to the growth rate. (Here, it is years.)
Filling in the given numbers, we have ...
35300 = 20000×1.029^t
35300/20000 = 1.029^t . . . . divide by 20,000
log(353/200) = t×log(1.029) . . . . take logarithms
log(353/200)/log(1.029) = t ≈ 23.01
It will be 23 years until the population reaches 35,300.
Answer: it will take 23 years.
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 = 20000
A = 35300
r = 2.5% = 2.5/100 = 0.025
Therefore
35300 = 20000(1 + 0.025)^t
35300/20000 = (1.025)^t
1.765 = (1.025)^t
Taking log of both sides to base 10
Log 1.765 = log1.025^t = tlog1.025
0.247 = 0.0107t
t = 0.247/0.0107
t = 23 years
