Question

A certain city has a population of p = 142,000e0.0141 where t is the time in years and t = 0 is the year 1990.

a. what was the population in the 2000? show your work.

Answer 1

The population of the city in the year 2000 is calculated by substituting t=10 into the given population growth formula and simplifying. This results in an approximate population of 163,556 people for the year 2000.

Step-by-step explanation:

To solve for the population of the city in the year 2000 given the formula p = 142,000e0.0141t, where t is the time in years since 1990, we first need to calculate the value of t for the year 2000. Since t = 0 corresponds to the year 1990, for the year 2000 we have t = 2000 - 1990 = 10 years.

We then plug t = 10 into the formula:

p = 142,000e(0.0141)(10)

Calculating the exponent:

0.0141 * 10 = 0.141

Now, raise e to this power:

e0.141 is approximately 1.1518 (using a calculator).

Multiply this by 142,000:

142,000 * 1.1518 = 163,555.6

Therefore, the population of the city in the year 2000 was approximately 163,556 people (after rounding).