How do you estimate the instantaneous rate of change in population in 2010 if a city's population (tens of thousands) is modeled by the function $p(t) = 1.2(1.05)^t$ where t is number of years since 2000?

Question

How do you estimate the instantaneous rate of change in population in 2010 if a city's population (tens of thousands) is modeled by the function $p(t) = 1.2(1.05)^t$ where t is number of years since 2000?

1 Answer

Impact of this question

8183 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-21T20:22:04

The instantaneous rate of change is nothing more than the derivative of your function; in one specific instant (as for you in year 2010) is the derivative evaluated at that point.
$p'(t)=1.2[1.05^xln(1.05)]$
At $t=10$
$p'(10)=0.09$ tens of thousands per year

Science

Math

Humanities

... and beyond

How do you estimate the instantaneous rate of change in population in 2010 if a city's population (tens of thousands) is modeled by the function $p(t) = 1.2(1.05)^t$ where t is number of years since 2000?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you estimate the instantaneous rate of change in population in 2010 if a city's population (tens of thousands) is modeled by the function p(t) = 1.2(1.05)^tp(t) = 1.2(1.05)^t where t is number of years since 2000?

1 Answer

Related questions

Impact of this question

How do you estimate the instantaneous rate of change in population in 2010 if a city's population (tens of thousands) is modeled by the function $p(t) = 1.2(1.05)^t$ where t is number of years since 2000?