Question

The population P = P(t) of Helm, can be modeled by

P(t) = 250,300e^kt
,
where t is the number of years since 2010. (t = 0 corresponds to the
year 2010.)
(a) Using the fact the population was about 267,000 in 2015, find k.
(Give an exact value and then round to 4 decimal places.
(b) According to the model using the approximate value of k, during
what year will the population
reach 300,000?

Answer 1

A.) 0.0129 = k

B.) 2024

Explanation:

A.)

267,000 = 250,300e^k5

267,000/250,300 = e^k5

1.0667 = e^k5

ln(1.0667) = lne^k5

ln(1.0667) = 5k

ln(1.0667)/5 = k

0.0129 = k

B.)

300,000 = 250,300^0.0129t

300,000/250,300 = e^0.0129t

1.1986 = e^0.0129t

ln(1.1986) = lne^0.0129t

ln(1.1986) = 0.0129t

ln(1.1986)/0.0129 = t

14.03 = t

so the year would be: 2024