Answer:
4.8%
Step-by-step explanation:
The population that grows with an annual percentage rate compounded continuously is given by: H = H° e^rt
Let the population be represented by H
The population reaches 1.1 times its previous size in 2 years.
So when t=2,
H = 1.1 H°
We substitute to obtain:
1.1 H° = H° e^r2
1.1 = e^2r
Take natural log to get:
In 1.1 = 2r
r = In 1.1 /2
r = 0.0477
Therefore the annual percentage rate is 4.8%
Answer:
Step-by-step explanation:
The formula for continuous compounding is expressed as
A = Pe(r x t)
Where
A represents the population after t years.
P represents the initial population.
r represents the rate of growth
t represents the time in years.
From the information given,
A = 1.1 × P = 1.1P
t = 2 years
Therefore,
1.1P = Pe(r x 2)
1.1P/P = e(r x 2)
1.1 = e(2r)
Taking ln of both sides of the equation, it becomes
Ln 1.1 = 2rlne
0.095 = 2r
r = 0.095/2
r = 0.0475
Therefore, the formula to find the annual percentage rate is
A = Pe(0.0475t)
