Question

The population of a city with a growth rate of 4% is 67,212 people. What will be the population of the city after 10 years? Use P=P0×ert
and round the answer to the nearest whole number. (1 point)
Responses

100,269
100,269

77,312
77,312

67,481
67,481

69,955

Answer 1

To calculate the population of the city after 10 years using the formula \( P = P_0 \times e^{rt} \), we will use the following values:

- \( P_0 = 67,212 \) (initial population)
- \( r = 0.04 \) (growth rate of 4%)
- \( t = 10 \) (time in years)
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.

Now we can compute it step by step:

1. Calculate \( rt \):
\[
rt = 0.04 \times 10 = 0.4
\]

2. Calculate \( e^{rt} \):
\[
e^{0.4} \approx 1.49182
\]

3. Now use the growth formula:
\[
P = 67,212 \times 1.49182 \approx 100,269.53
\]

Finally, rounding to the nearest whole number gives us:
\[
P \approx 100,270
\]

Thus, the population of the city after 10 years will be approximately **100,270**.

From the given responses, the correct answer is:
**100,269** (closer number provided in the options).