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Gnom [1K]
3 years ago
7

A particular​ country's exports of goods are increasing exponentially. The value of the​ exports, t years after 2008​, can be ap

proximated by ​V(t)equals1.4 e Superscript 0.039 t where tequals0 corresponds to 2008 and V is in billions of dollars.
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
3 0

Answer:

a) For 2008 we have that t = 2008-2008 = 0 and we have:

V(0)= 1.4e^{0.039*0}= 1.4

For 2022 we have that t = 2022-2008=14 and if we replace we got:

V(12) = 1.4 e^{0.039*14}=2.417

b) 2.8 = 1.4 e^{0.039 t}

We can divide both sides by 1.4 and we got:

2 = e^{0.039 t}

Now natural log on both sides:

ln (2) = 0.039 t

t = \frac{ln(2)}{0.039}= 17.77 years

Step-by-step explanation:

For this case we have the following model given:

V(t) = 1.4 e^{0.039 t}

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:

V(0)= 1.4e^{0.039*0}= 1.4

For 2022 we have that t = 2022-2008=14 and if we replace we got:

V(12) = 1.4 e^{0.039*14}=2.417

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:

2.8 = 1.4 e^{0.039 t}

We can divide both sides by 1.4 and we got:

2 = e^{0.039 t}

Now natural log on both sides:

ln (2) = 0.039 t

t = \frac{ln(2)}{0.039}= 17.77 years

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