Hi,
I had a question about exponential growth. The problem says: The population in Woonsocket is 43,500. Every year the population increases by 2%. Write the exponential equation that represents this situation. I put that the equation was 43,500 (1+.2)^y (y standing for how many years go by as the population increases). Would this equation be correct? When I plug in the numbers: 43,500 (1+.2)^1, I got 52,200. That doesn't sound right, considering that the population only increases 2%. Did I do the problem wrong or does anyone know how I can fix it?
2 % = 0.02
You multiplyed by 0.2 -- which is 20%.
Thank you. :)
You're welcome. :-)
wow this old question, but 2% as decimal is 0.02. 0.2 or .2 is 20% as decimal.
here is explanation:
43500(1+0.2)^1.
43500(1.2)^1.
43500 * 1.2 = 52,200.
Your work correct. Nothing wrong.
To represent exponential growth, you need to use the formula:
A = P(1 + r)^t
Where:
- A represents the final amount (population in this case)
- P is the initial amount (population in the first year)
- r is the rate of growth (expressed as a decimal)
- t is the time period (in this case, the number of years)
In your case, the initial population (P) is 43,500, and the rate of growth (r) is 2% or 0.02 (since 2% can be expressed as 0.02).
So, the correct formula to represent the population growth would be:
A = 43,500(1 + 0.02)^t
Now, let's calculate the population after 1 year:
A = 43,500(1 + 0.02)^1
A = 43,500(1.02)
A ≈ 44,470.
So, the population estimation after 1 year would be approximately 44,470 (rounded to the nearest person).
To calculate the population after a different number of years, simply replace the value of t in the equation with the desired number of years.