Question

A​ country's travel exports​ (good and services that international travelers buy while visiting the​ country) are increasing exponentially. The value of such​ exports, t years after​ 2011, can be approximated by ​V(t)equals115.31 e Superscript 0.087 t​, where V is in billions of dollars. ​a) Estimate the value of the​ country's travel exports in 2019 and 2020. ​b) Estimate the growth rate of the​ country's travel exports in 2019 and 2020.

Answer 1

The equation given is:

`V(t) = 115.31e^(0.087t)`

Part A

As t represents the years after 2011, and we need to calculate exports in 2019 and 2020.

For 2019

t = 2019 - 2011 = 8

Substitute in the given equation:

`V(8)=115.31e^(0.087((8))\\V(8)=230.62`

For 2020

t = 2020-2011 = 9

`V(9)=115.31e^(0.087((9))\\V(9)=251.38`

Part B

First calculate V(0)

`V(0)=115.31e^(0.087((0))\\V(0)=115.31`

Formula for the growth rate is given by:

Growth Rate = (present/past)^1/t - 1

`G.R=((Present)/(Past))^{(1)/(t)}-1`

Where

Past = 115.31

Calculate Growth Rate for 2019

Present = 230.62

t = 8

Substitute in the equation of Growth rate:

`G.R=((230.62)/(115.31))^{(1)/(8)}-1\\G.R =1.09-1\\G.R = 0.09\\`

In percentage, the growth rate is:

G.R = 9.05 %

Calculate Growth Rate for 2020

Present = 251.38

t = 9

Substitute in the equation of Growth rate:

GR= 9.05%