The population P of a city has been increasing at an annual rate of 1.4%. It's population was 173 thousand in 1992.

A. Find a formula for P(t), where t is the year and P is in thousands.
B. Estimate the population in 2010, to the nearest thousand.
C. In what year did the population reach 188 thousand?

A. To find a formula for P(t), we need to start with the initial population and account for the annual growth rate.

Let's define P₀ as the initial population in the year 1992 (173 thousand). We can express this as P₀ = 173.

The annual growth rate is 1.4%. To account for this, we multiply P₀ by (1 + r), where r is the growth rate expressed as a decimal. In this case, r = 1.4% = 0.014.

So, the formula for P(t) is: P(t) = P₀ * (1 + r)^t

B. To estimate the population in 2010, we need to substitute t = 2010 into the formula and round the result to the nearest thousand.

Using the formula from part A:
P(2010) = P₀ * (1 + r)^2010

Substituting the given values:
P(2010) = 173 * (1 + 0.014)^2010

Using a calculator, we can evaluate this expression and round the result to the nearest thousand.

C. To find the year when the population reached 188 thousand, we need to solve the equation P(t) = 188.

Using the formula from part A:
P(t) = 173 * (1 + 0.014)^t

Setting this equation equal to 188:
188 = 173 * (1 + 0.014)^t

We can use logarithms or trial and error to find the value of t that makes the equation true.