The adult population of a city is 1,150,000. A consultant to a law firm uses the function P(t) 1,150,000(1 – e–0.03t) to estimate the number of people P(t) who have heard about a major crime t days after the crime was first reported. About how many days does it take for 60% of the population to have been exposed to news of the crime?
+128732 P(t) = 1,150,000(1 – e–0.03t)
60% of the population = 690,000 ...... so we have....
690,000 = 1,150,000(1 – e–0.03t) divide both sides by 1,150,000
.60 = (1 - e^(-0.03t)) rearrange
.40 = e^(-0.03t) take the ln of each side
ln .40 = ln e^(-0.03t) and we can write
ln .40 = -.0.03t divide both sides by -0.03
ln .40 / -0.03 = t = about 31 days
+128732 P(t) = 1,150,000(1 – e–0.03t)
60% of the population = 690,000 ...... so we have....
690,000 = 1,150,000(1 – e–0.03t) divide both sides by 1,150,000
.60 = (1 - e^(-0.03t)) rearrange
.40 = e^(-0.03t) take the ln of each side
ln .40 = ln e^(-0.03t) and we can write
ln .40 = -.0.03t divide both sides by -0.03
ln .40 / -0.03 = t = about 31 days
