A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula $P = A e^{k t}$ $P=Ae^(kt)$ ?

Question

A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula $P = A e^{k t}$ $P=Ae^(kt)$ ?

1 Answer

Impact of this question

4584 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-28T12:16:42

$207$ $207$ million

Explanation:

For this problem, we have the final population $P$ $P$ , the starting population $A$ $A$ , and the time passed $t$ $t$ .

We still need to determine the value of the growth factor $k$ $k$ .

This can be done using the information for the years $1994$ $1994$ and $2002$ $2002$ .

In this case, $A$ $A$ will be $195$ $195$ million (the population in $1994$ $1994$ ), $P$ $P$ will be $199$ $199$ million (the population in $2002$ $2002$ ), and $t$ $t$ will be $8$ $8$ years (the number of years between $1994$ $1994$ and $2002$ $2002$ ):

$\Rightarrow P = A e^{k t}$ $Rightarrow P = A e^(k t)$

$\Rightarrow 199 = 195 e^{k \times 8}$ $Rightarrow 199 = 195 e^(k times 8)$

$\Rightarrow \frac{199}{195} = e^{8 k}$ $Rightarrow frac(199)(195) = e^(8 k)$

Applying $ln$ $ln$ to both sides of the equation:

$\Rightarrow ln (\frac{199}{195}) = ln (e^{8 k})$ $Rightarrow ln(frac(199)(195)) = ln(e^( 8k))$

Using the laws of logarithms:

$\Rightarrow 8 k ln (e) = ln (199) - ln (195)$ $Rightarrow 8 k ln(e) = ln(199) - ln(195)$

$\Rightarrow 8 k = ln (199) - ln (195)$ $Rightarrow 8 k = ln(199) - ln(195)$

$\Rightarrow k = \frac{ln (199) - ln (195)}{8}$ $Rightarrow k = frac(ln(199) - ln(195))(8)$

$therefore k = 0.00253815825$

Now, let's use this information to determine $P$ in $2016$ .

$A$ will still be $195$ million, but $t$ will be $22$ years.

$Rightarrow P = 195 e^(0.00253815825 times 22)$

$Rightarrow P = 195 e^(0.0558394815)$

$Rightarrow P = 195 times 1.057427933$

$therefore P = 206.19844694$

Therefore, the population in $2016$ will be around $207$ million.

Science

Math

Humanities

... and beyond

A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula $P = A e^{k t}$ $P=Ae^(kt)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula P=Ae^(kt)P=AektP=Ae^(kt)?

1 Answer

Explanation:

Related questions

Impact of this question

A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula $P = A e^{k t}$ $P=Ae^(kt)$ ?