Final answer:
To find when the population reaches 214 thousand, set the equation A=139e^0.048t equal to 214 and solve for t, which involves dividing the natural logarithm of 214/139 by 0.048.
Step-by-step explanation:
The student's question is about determining when the population of a city, modeled by the equation A=139e^0.048t, will reach 214 thousand. To solve for t, we set the model equal to 214 and solve for t:
- 214 = 139e^0.048t
- e^0.048t = 214/139
- 0.048t = ln(214/139)
- t = ln(214/139) / 0.048
Calculating t, we find the number of years after 1998 that the population reaches 214 thousand. The student should use a calculator to compute the natural logarithm and divide by 0.048 to get the result.