Final answer:
To solve the equation A = 261e^(0.024t) and find when the population of the city will reach 316 thousand, we can substitute 316 for A and solve for t. The population of the city will reach 316 thousand in the year 2027.
Step-by-step explanation:
To solve the equation A = 261e^(0.024t), where A represents the population of the city in thousands and t represents the number of years after 2011, we need to find the value of t when A is equal to 316. We can do this by substituting 316 for A and solving for t:
316 = 261e^(0.024t)
Divide both sides by 261:
1.210.73=e^(0.024t)
Take the natural logarithm of both sides:
ln(1.210.73) = 0.024t
Divide both sides by 0.024:
t = ln(1.210.73) / 0.024
Using a calculator, we find that t is approximately 16.015 years. Since the population is measured in thousands and we are looking for the number of years after 2011, we add 2011 to t:
2011 + 16.015 = 2027.015
Therefore, the population of the city will reach 316 thousand in the year 2027. The correct answer is A. 2027.