Question

A countries population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential growth formula round your answer to the nearest million. P=Ae^kt

Answer 1

Answer:

The population in 2017  is 171 million

Step-by-step explanation:

Let's assume population starts from 1991

so,

initial population is 147 million

so, $A=147$

we can use formula

$P=Ae^{kt}$

we can plug A=147

$P=147e^{kt}$

In 1998:

t=1998-1991=7

$P=153$

now, we can plug these values into formula and find k

$153=147e^{7k}$

Divide both sides by 147

$\frac{147e^{7k}}{147}=\frac{153}{147}$

$e^{7k}=\frac{51}{49}$

$\ln \left(e^{7k}\right)=\ln \left(\frac{51}{49}\right)$

$k=\frac{\ln \left(\frac{51}{49}\right)}{7}$

$k=0.00572$

now, we can plug it back

and we get

$P=147e^{0.00572t}$

In 2017:

t=2017-1991=26

we can plug it and find P

$P=147e^{0.00572\times 26}$

$P=170.57$

So,

The population in 2017  is 171 million