+0

# The adult population of a city is 1,150,000. A consultant to a law firm uses the function P(t)

0
894
1

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?

Guest May 28, 2015

#1
+85720
+10

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

CPhill  May 28, 2015
Sort:

#1
+85720
+10

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

CPhill  May 28, 2015

### 17 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details