I am stuck in exponential growth and decay. Here is an example. Can someone tell me how to do this step-by-step please? Here it is...

The population of Mexico has been increasing at an annual rate of 1.7%. If the population of Mexico was 100,350,000 in the year 2000, predict its population in 2012.

I tried this many times but kept failing at it. Can someone please help me? Thanks

The examples in my book didn't help and didn't even mention anything remotely simialr to this problem.

Pt = Po(1 + rt),

r = 1.7% / 100% = 0.017 = Annual % increase expressed as a decimal.

t = 2012 - 2000 = 12yrs.

rt = 0.017/yr * 12yrs = 0.204.

Pt = 100.35*10^6(1.204),
Pt = 120.8214*10^6 = 120,821,400 = population in 2012.

Thankyou so mjch for the help. The book says 122,848,204 ,but the problem says for me to estimate so basically anything close to it would work. Right? Like 120,821,400.

Sure, I can help you with that!

To predict the population of Mexico in 2012, we can use the formula for exponential growth:

P(t) = P(0) * (1 + r)^t

Where:
- P(t) is the population at time t
- P(0) is the initial population
- r is the growth rate expressed as a decimal
- t is the time period

In this case, the initial population (P(0)) is 100,350,000, the growth rate (r) is 1.7% or 0.017 (expressed as a decimal), and we want to find the population at year 2012, which is 12 years after 2000 (t = 12).

Let's plug in these values into the formula:

P(2012) = 100,350,000 * (1 + 0.017)^12

Now, we need to solve this equation to find the population of Mexico in 2012. Here are the steps:

Step 1: Calculate the growth rate plus 1:
1 + 0.017 = 1.017

Step 2: Raise this result to the power of 12:
(1.017)^12 ≈ 1.219

Step 3: Multiply the initial population by the result:
100,350,000 * 1.219 ≈ 122,799,150

So, according to the given annual growth rate, the predicted population of Mexico in 2012 will be approximately 122,799,150.

I hope this helps! Let me know if you have any further questions.