Solve the problem. \[ \begin{array}{l}\text { 9) The formula } \mathrm{A}=130 \mathrm{e}^{0.022 t} \text { models the population of a particular city, in thousands, } t \text { years after } \\ \text { 1998. When will the population of the city reach } 173 \text { thousand? }\end{array} \]

To find out when the population will reach 173 thousand, we can set \( A = 173 \) in the given formula: \[ 173 = 130 e^{0.022t} \] Now, we need to solve for \( t \). First, divide both sides by 130: \[ \frac{173}{130} = e^{0.022t} \] Calculating the left side: \[ \frac{173}{130} \approx 1.330769 \] Now take the natural logarithm of both sides: \[ \ln\left(\frac{173}{130}\right) = \ln(e^{0.022t}) \] This simplifies to: \[ \ln\left(\frac{173}{130}\right) = 0.022t \] Now we can calculate \( \ln\left(\frac{173}{130}\right) \): \[ \ln(1.330769) \approx 0.262364 \] Now, solve for \( t \): \[ t = \frac{0.262364}{0.022} \approx 11.93 \] This means that approximately 11.93 years after 1998, the population will reach 173 thousand. Rounding up, we can say the population will reach this number in the year: \[ 1998 + 12 \approx 2010 \] Thus, the population will reach 173 thousand around the year 2010.