Ask Question
3 February, 13:14

A town has a population of 6000 people in the year 2009 and is growing at a rate of 3% a year. Let t denote the time in years after 2009, so t = 0 denotes 2009. Let f be the function that, to each year t, assigns the population of the town in year t. In the text box below, enter a formula for f (t). Your entry must begin with f (t) = and to the right of the equals sign you should enter the formula for f (t). Your answer must be mathematically valid. For example, if you believe that

f (t) = t^ - 3 + 5 * t - 3,

then in the text box you should enter f (t) = t^ (-3) + 5*t-3. After entering your answer, click the Save Answer button.

Response to your input section.

Enter The Value Of k Here:

+3
Answers (1)
  1. 3 February, 16:07
    0
    f (t) = 6000*1.03^t k = 0.0295588

    Step-by-step explanation:

    The formula for exponential growth can be written a couple of different ways. One I prefer uses the problem numbers directly:

    population = (initial population) * (growth factor) ^t

    Here, the initial population is 6000, and the growth factor is 1+3% = 1.03. Then the function can be written as ...

    f (t) = 6000·1.03^t

    __

    Another way to write the function is using the form ...

    f (t) = (initial population) * e^ (kt)

    where k is the natural logarithm of the growth factor. In this form, we have ...

    k = ln (1.03)

    k ≈ 0.0295588

    so the function would be written ...

    f (t) = 6000·e^ (0.0295588t)
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A town has a population of 6000 people in the year 2009 and is growing at a rate of 3% a year. Let t denote the time in years after 2009, ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers