The formula A=298e^0.027t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 370 thousand?
Solve for t over the real numbers:
298 e^(0.027 t) = 370000
298 e^(0.027 t) = 298 e^(27 t/1000):
298 e^((27 t)/1000) = 370000
Divide both sides by 298:
e^((27 t)/1000) = 185000/149
Take the natural logarithm of both sides:
(27 t)/1000 = log(185000/149)
Multiply both sides by 1000/27:
Answer: | t = 1000/27 log(185000/149 t=263.8570
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