Question

The function P(t)=25,000(1.1023)t2 can be used to model the population in the town of Madison t years from now. Interpret the function in terms of the context for this situation.

Answer 1

• t=number of years

Lets find year wise population for example

• let years be 3
• t=3

`\\ \sf{:}\longrightarrow P(3)=25,000(1.1023)3^2`

`\\ \sf{:}\longrightarrow P(3)=27557.5(9)`

`\\ \sf{:}\longrightarrow P(3)=248017.5`

Answer 2

A growth function has the following form.

where = Original amount,

r = annual rate of change,

n = number of periods,

t = time in years

Since the time is in years, we need to convert t into days. We know that 1 year = 365 days. So t years = 365t days.

So in this case, n = 365, r = 0.0095.

Then the function is rewritten as follows.

The daily growth rate would be

Explanation: