Question

The population of a particular city is given by the function P(t) = 12,500(1.04)4t, where t is time in years and P(t) is the population after t years.

Part A: Examine the function. What is the initial population and the percentage growth rate (rounded to the nearest whole percent)?

Part B: What is the population size (rounded to the nearest whole person) in 10 years?

Part C: How would the population size be affected if 0 < r < 1? Explain

Answer 1

First, a bit of housekeeping is necessary here:

the proper way to write P(t) = 12,500(1.04)4t

is ... \[P(t) = 12,500(1.04)^{4t}\]

Answer 2

You are likely to work with exponential functions enough to make it worth your while to indicate exponentiation properly.

Answer 3

Ok

Answer 4

Part A: Examine the function. What is the initial population and the percentage growth rate (rounded to the nearest whole percent)? The initial population is clearly given; you just need to know where to find it.

Similarly, the annual growth rate can be derived directly from the given equation.

Answer 5

Isnt the growth rate 1%?

Answer 6

If you have a textbook or access to online learning resources, search for "compound interest." No, the growth rate is not 1%.

Answer 7

I know the initial population is 12,500

Answer 8

that's correct. Very good!

Answer 9

Then it must be 4%

Answer 10

Is the population increasing or decreasing, and how do you know this?

Answer 11

Am i right?

Answer 12

Its increasing

Answer 13

Hello?

Answer 14

That might help a bit.