A countrys population in 1995 was 56 million in 2002 it was 59 million. Estimate the population in 2016. Exponential growth formula
your function will look like this:
population = 56 e^kt, where t = 0 represents 1995
then 2002 ---> t = 7
and 2016 ---> t = 21
for t = 7 (2002)
59 = 56 e^7k
1.05357... = e^7k
7k = ln 1.05357.. = .052185753
k = appr .0074551
pop = 56 e^(.0074551t)
sub in t = 21 and evaluate
To estimate the population in 2016 using the exponential growth formula, we need to know the initial population in 1995, the growth rate, and the number of years between 1995 and 2016.
Step 1: Determine the growth rate per year
The growth rate per year can be calculated by taking the natural logarithm of the population in 2002 divided by the population in 1995:
Growth rate = ln(P₂/P₁) / (T₂ - T₁)
Where:
P₁ = Population in 1995 (56 million)
P₂ = Population in 2002 (59 million)
T₁ = Year 1995
T₂ = Year 2002
Plugging in the values, we get:
Growth rate = ln(59/56) / (2002 - 1995)
Step 2: Calculate the population in 2016
Using the exponential growth formula:
P(t) = P₁ * e^(r*t)
Where:
P(t) = Population at time t
P₁ = Population at the initial time
r = Growth rate per year
t = Number of years from the initial time to the desired time
Plugging in the values, we have:
P(2016) = P₁ * e^(r * (2016 - 1995))
Now, you can calculate the estimated population in 2016 using the formula.