rate of change word problem

[Sophie]

Hello could someone confirm my answer to the following question. I attempted it last week without understanding the chain rule and am trying it again.

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 (1.018)^t ln1.018


growth of population at start of 1990:
P'(0) = 1.05 (1.018)^1 ln1.018
P'(0) = 59.916
At the strat of 1990 the popultaion was growing by 59.916 million per year

growth of population at start of 1995
P'(5) = 1.05 (1.018)^5 ln1.018
= 3041.557

At the strat of 1995 the popultaion was growing by 3041.557 million per year


Thanks Sophie

 

[galactus]

Hello could someone confirm my answer to the following question. I attempted it last week without understanding the chain rule and am trying it again.

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 (1.018)^t ln1.018


growth of population at start of 1990:
P'(0) = 1.05 (1.018)^1 ln1.018
P'(0) = 59.916
At the strat of 1990 the popultaion was growing by 59.916 million per year

growth of population at start of 1995
P'(5) = 1.05 (1.018)^5 ln1.018
= 3041.557

At the strat of 1995 the popultaion was growing by 3041.557 million per year


Thanks Sophie

I think you erred a bit, Sophie. The population is growing by over 3 billion a year. Humans are huge breeders, but not quite that bad...yet.

\(\displaystyle \L\\\frac{d}{dt}\left[\frac{21}{20}(\frac{509}{500})^{t}\right]=\frac{21ln(\frac{509}{500})(\frac{509}{500})^{t}}{20}\)

At t=5, we have 0.020479580012

 

[Sophie]

Thanks, I appear to have made a silly mistake, not sure how, just did it agin and I get the same as you.

Thanks Sophie