Rate of change word problem

[Sophie]

Hello could someone confirm my answer to the following question.

The population of a country, measured in million, is given by p=1.05(1.018)^t where t is the number of years since the start of 1990. According to this model, how fast is the population growing at the start of 1990 and at the start of 1995? Give units.

P(t) = 1.05(1.018)^t
P'(t) = (1.05 * t1.018^(t-1)) + (1.018^t * 0)
P'(t) = 1.05 * t1.018^(t-1)

growth of population at start of 1990:
P'(0) = 0

growth of population at start of 1995
P'(5) = 1.05 * (5*1.018^4)
= 5.638 Million/year

Thanks Sophie

 

[mark07]

You're confusing the power rule and exponential derivatives!

\(\displaystyle \L \frac{d}{dx}\left( x^5 \right) = 5 x^4\)

but

\(\displaystyle \L \frac{d}{dx}\left( 5^x \right) = 5^x \ln 5\)

Take the derivatives again...

 

[Sophie]

Thanks

I am not sure I have covered this yet and am not sure why I am being asked the question now. I will cover the next couple of chapters and try again.

Thanks