Question

A research study in 2000 found that there were 440 coyotes in a given region. The coyote population is expected to grow at a rate of 17% each year. In what year will the population first exceed 10,000?

Answer 1

Let t = # of years since 2000
Then we have:
y=440(1+0.17)^t

Answer 2

so y=514^2 ??

Answer 3

do u know how to take ln of both sides?

Answer 4

10000=440(1+0.17)^t

Answer 5

\[\frac{ 10000 }{ 440 }=(1+0.17)^t\]

Answer 6

then we take ln of both sides\[\ln(22.73)=t \ln(1+0.17)\]

Answer 7

\[\frac{ \ln(22.73) }{ \ln(1+0.17)}=t\]

Answer 8

what do u get?

Answer 9

22.9?

Answer 10

r u sure i am getting 19.89

Answer 11

dont use log use ln

Answer 12

on ur calculator

Answer 13

so basically u roud this up and u will get 20 years so 2000+20 which will equal 2020

Answer 14

so in 2020 the population first exceed 10,000?

Answer 15

um..im confused

Answer 16

the answer is 20?

Answer 17

no it asks in what year the population will exceed 10000

Answer 18

okay sorry i meant 2020

Answer 19

yes thats correct

Answer 20

yay omg thank you!!

Answer 21

it was 2019 but thanks for helping me understand it lol

Answer 22

opps srry i thought cause its coming 19.89 it should be rounded up