1. ## logs help urgent

Hey.

Could someone help me on this question because i am stuck. Am i doing the wrong thing?

Write down the function which could be used to estimatethe GDP of a particular country in t years time, when the current GDP equals A units, and which grows at r% per annum, where growth is continuous.

Use this function, estimate the annual average percentage rate of growth r, when GDP of a country grows from 250 units to 420 units in 8 years.

GDP = Ae^8

lnGDP = lnA + lne^8

= 170 + 2980

= 3150

This doesn't look right could someone tell me what im doing wrong?

THanks

2. Originally Posted by Stem01
Hey.

Could someone help me on this question because i am stuck. Am i doing the wrong thing?

Write down the function which could be used to estimatethe GDP of a particular country in t years time, when the current GDP equals A units, and which grows at r% per annum, where growth is continuous.

Use this function, estimate the annual average percentage rate of growth r, when GDP of a country grows from 250 units to 420 units in 8 years.

GDP = Ae^8

lnGDP = lnA + lne^8

= 170 + 2980

= 3150

This doesn't look right could someone tell me what im doing wrong?

THanks
1. I would use:

$\displaystyle GDP(t)=A \cdot \left(1+\dfrac r{100}\right)^t$

2. You'll get an approximate value if you use:

$\displaystyle GDP(t)=A \cdot e^{\left(\frac r{100}\right) \cdot t}$

3. With your question you get:

$\displaystyle 420=250 \cdot e^{\left(\frac r{100}\right) \cdot 8}$

$\displaystyle \dfrac{420}{250}= e^{\left(\frac r{100}\right) \cdot 8}$

$\displaystyle \ln(420)-\ln(250)= 8 \cdot \frac r{100}$

$\displaystyle \dfrac{100(\ln(420)-\ln(250))}8= r$

$\displaystyle \boxed{r\approx 6.485\ \%}$

3. Thanks soo much for your help.

Aothe average percentage growth rate = 6.5%