Question

A population of coyotes in a country is represented by the equation w(t)=80(0.98)^t, where t is the number of years since 1998. In what year will the population be 50 wolves?

Answer 1

Answer:

2021

Step-by-step explanation:

w(t) = 80(0.98)^t

w(t) = 50

50/80 = (0.98)^t

5/8 = (0.98)^t

log(5/8) = log((0.98)^t)

Property of logs allows the exponent to be move to the front so,

log(5/8) = t*log(0.98)

solve for t

t = (log(5/8))/(log(0.98))

so t = 23.264

1998 + t = 2021.264

Round to 2021 because that's they year it is present in.