The population of Winnemucca Nevada can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What was the population in 1990? By what percent did the population increase by each year?

To be honest, this question is very simple. You can look at the number after the decimal in (1.04) to find the percentage. just multiply the .04 by 100 to find the percentage.

As for the population in 1990, since the year is 1990, t would be equal to 0, (no years since 1990 from 1990)

P= 6191 (1.04)^0
P=?

No, anything with a power of 0 is 1.

To find the population in 1990, we need to substitute t=0 into the population growth model equation.

Given:
P = 6191(1.04)^t
t = number of years since 1990
P = population

In 1990, t=0 since it is the starting point. So, we substitute t=0 into the equation:
P = 6191(1.04)^0
P = 6191(1)
P = 6191

Therefore, the population in Winnemucca, Nevada, in 1990 was 6,191.

Now, to calculate the percent increase each year, we need to compare the population from one year to the next.

The population growth model given is P = 6191(1.04)^t, where t is the number of years since 1990.

To find the percent increase each year, we can compare the population of one year to the next by using the formula:

Percent Increase = (New Population - Old Population) / Old Population * 100

In this case, we compare the population each year to the previous year. We can start by calculating the percent increase for the first year:

Percent Increase for year 1:
New Population = P for t=1 = 6191(1.04)^1
Old Population = P for t=0 = 6191

Percent Increase for year 1 = (6191(1.04)^1 - 6191) / 6191 * 100

Now, let's simplify and calculate:

Percent Increase for year 1 = (6191(1.04) - 6191) / 6191 * 100
Percent Increase for year 1 = (6433.44 - 6191) / 6191 * 100
Percent Increase for year 1 = 242.44 / 6191 * 100
Percent Increase for year 1 ≈ 3.92%

Therefore, the population in Winnemucca, Nevada, increased by approximately 3.92% each year.

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