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In-s [12.5K]
3 years ago
6

A countrys population in 1990 was 145 million. In 1998 it was 151 million. Estimate the population in 2015 using the exponential

growth formula. Round your answer to the nearest million
Mathematics
1 answer:
alexandr402 [8]3 years ago
5 0

Answer:

The population in 2015 will be 165 million.

Step-by-step explanation:

The exponential growth formula is given by:

f(t) = a(1 + r)^{\Delta t}

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:

151 = 145(1 + r)^{1998-1990}      

Using logarithm:                                    

ln(151) = ln(145) + 8[ln(1 + r)]  

ln(1 + r) = \frac{ln(151) - ln(145)}{8}                        

ln(1 + r) = 5.0683 \cdot 10^{-3}          

Using exponential:          

e^{ln(1 + r)} = e^{5.0683 \cdot 10^{-3}}

r = 5.081 \cdot 10^{-3}        

Now, we can find the estimated population in 2015:

f(t) = 151(1 + 5.081 \cdot 10^{-3})^{2015-1998}              

f(t) = 165              

Therefore, the population in 2015 will be 165 million.

I hope it helps you!

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