Question

The projected population of a certain ethnic group(in millions) can be approximated by \( p(t)=39.11(1.013)^{\mathrm{t}} \) where \( \mathrm{t}=0 \) corresponds to 2000 and \( 0 \leq t \leq 50 \). a.

Answer 1

Step-by-step explanation:

It looks like you want to work with the population projection formula \( p(t) = 39.11(1.013)^t \) where \( t \) corresponds to years since 2000 (where \( t = 0 \) corresponds to 2000).

Let's address your question:

a. If you want to find the projected population for a specific year, say \( t = 10 \), you can simply plug this value into the formula:

\( p(10) = 39.11(1.013)^{10} \)

Calculate the right-hand side to find the population projection for the year 2010 (10 years after 2000).

b. To find the rate of population growth, you can look at how the population changes from one year to the next. Calculate \( p(t + 1) - p(t) \) to find the population change from year \( t \) to \( t + 1 \). This will give you the annual growth rate.

c. If you want to find the year when the projected population reaches a certain value, say \( p(t) = 50 \) million, you need to solve for \( t \) in the equation:

\( 50 = 39.11(1.013)^t \)

You can use logarithms to solve for \( t \) in this exponential equation. Once you find \( t \), remember to add it to 2000 to get the corresponding year.

If you have specific values or calculations you'd like to perform using this formula, please provide those details, and I can assist you further.