Answer:
The population in 2015 will be 165 million.
Step-by-step explanation:
The exponential growth formula is given by:
[tex] f(t) = a(1 + r)^{\Delta t} [/tex]
Where:
a: is the initial population
r: is the rate of increase
Δt: is the time
With the initial information we can find the rate:
[tex] 151 = 145(1 + r)^{1998-1990} [/tex]
Using logarithm:
[tex] ln(151) = ln(145) + 8[ln(1 + r)] [/tex]
[tex] ln(1 + r) = \frac{ln(151) - ln(145)}{8} [/tex]
[tex] ln(1 + r) = 5.0683 \cdot 10^{-3} [/tex]
Using exponential:
[tex] e^{ln(1 + r)} = e^{5.0683 \cdot 10^{-3}} [/tex]
[tex] r = 5.081 \cdot 10^{-3} [/tex]
Now, we can find the estimated population in 2015:
[tex] f(t) = 151(1 + 5.081 \cdot 10^{-3})^{2015-1998} [/tex]
[tex] f(t) = 165 [/tex]
Therefore, the population in 2015 will be 165 million.
I hope it helps you!
