Answer:
a) For 2008 we have that t = 2008-2008 = 0 and we have:
[tex] V(0)= 1.4e^{0.039*0}= 1.4[/tex]
For 2022 we have that t = 2022-2008=14 and if we replace we got:
[tex] V(12) = 1.4 e^{0.039*14}=2.417[/tex]
b) [tex] 2.8 = 1.4 e^{0.039 t}[/tex]
We can divide both sides by 1.4 and we got:
[tex] 2 = e^{0.039 t}[/tex]
Now natural log on both sides:
[tex] ln (2) = 0.039 t[/tex]
[tex] t = \frac{ln(2)}{0.039}= 17.77 years[/tex]
Step-by-step explanation:
For this case we have the following model given:
[tex] V(t) = 1.4 e^{0.039 t}[/tex]
Where V represent the exports of goods and the the number of years after 2008.
Part a
Estimate the value of the country's exports in 2008 and 2022
For 2008 we have that t = 2008-2008 = 0 and we have:
[tex] V(0)= 1.4e^{0.039*0}= 1.4[/tex]
For 2022 we have that t = 2022-2008=14 and if we replace we got:
[tex] V(12) = 1.4 e^{0.039*14}=2.417[/tex]
Part b
What is the doubling time for the value of the country's exports.
For this case we can set up the following condition:
[tex] 2.8 = 1.4 e^{0.039 t}[/tex]
We can divide both sides by 1.4 and we got:
[tex] 2 = e^{0.039 t}[/tex]
Now natural log on both sides:
[tex] ln (2) = 0.039 t[/tex]
[tex] t = \frac{ln(2)}{0.039}= 17.77 years[/tex]
