Question

4.5.13 2000 Pa Complete the table shows the right for the population growth for a certain country Projected Growth Rae Projected 2017 Population on Roof decimal places andet)

Answer 1

Uploaded image was unclear. But the steps are as follows:

If Population is increasing over time: Growth Funtion=$\large N(t) = N_{0}(1+k)^{t}$

If population is decreasing over time: Decay Function =

N(t) = No(1 - k)'

where N0 is initial population at t = 0, N(t) is population at time t, k is growth/decay rate.

Population in 2003 = 47.1 milion

Projected population in 3037 = 29.5 mllion

in 2003 --> t = 0

in 2037 --> t = 34

Since population is decreasing,

N(t) = No(1 - k)'

$\large 29.5=47.1(1-k)^{34}$

34 29.5 47.1 =(1-k)

$\large 0.626=(1-k)^{34}$

$\large ln(0.626)=ln[(1-k)^{34}]$

$\large -0.468=34ln(1-k)$

$\large -0.01376=ln(1-k)$

$\large e^{-0.01376}=(1-k)$

0.9863334 = 1 - k

k = 1 - 0.9863334

k = 0.0136666

k = 1.3667%

This is decay rate. So growth rate is -1.3667%