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?

Question

Mathematics

Tristan Fuller

30 August, 10:58

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?

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Answers (1)

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Mya · Answer 1

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.