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?

Question

Mathematics

Greyson Clark

17 April, 08:32

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?

+4

Answers (1)

Know the Answer?

Alana Haas · Answer 1

A.) 0.0129 = k

B.) 2024

Step-by-step 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