Exponential Equations 14

Question

Let  be the population of a town  years after the year 2000.Estimate in which year the population will reach 7351.Year = 

Answer 1

Stephanie

P(t) = 6000 (1.07)^t

We need t when P(t) = 7351

7351 = 6000 (1.07)^t

7351/6000 = 1.07^t

log (7351/6000) = t log (1.07)

t = log (7351/6000) / log (1.07) = 3.001491956

t = 3, year is 2000 + 3 = 2003

^{t = 4, year is 2004}

As our calculated t is between 3 and 4, the population becomes 7351 during the year 2003

Mike