A report tells us that in 2009, there were 870 gray wolves in Idaho, b

CMIIh

CMIIh

Answered question

2021-08-16

A report tells us that in 2009, there were 870 gray wolves in Idaho, but that the population declined by 19% annual rate of decrease continues.
a) Find an exponential model that gives the wolf population W as a function of the time t in years since 2009.
W=870(1.19)t
b) It is expected that the wolf population cannot recover if there are fewer than 25 individuals. How long must this rate of decline continue for the wolf population to reach 25?

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-08-17Added 117 answers

Given: The number of gray wolves in Idalho in year 2009 was 870.
It is given that population decreases annually at rate 19%.
To find:
a) To find an exponential models that gives wolves population W as a function of time t in years since 2009.
b) Number of years in which population of wolves reaches to 25.
Solution: We know that when population decline continuosly then population after time t years is given as:
W=P0(1r)t, where W is population after time t years, P_0 is initial population and r is rate of decline
We have given, P0=870
r=19%
=19100
=0.19
Therefore, an exponential models that gives wolves population is:
W=870(10.19)t
=870(0.81)t
Now, we have to find t when W=25
25=870(0.81)t
(0.81)t=25870
(0.81)t=0.028
log(0.81)t=log(0.028)
tlog(0.81)=log(0.028)
t(0.091)=1.55
t=1.550.091
t=17.03
Therefore, number of years the population will declined to 25 is 17.03 years.

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