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Sagot :
Answer:
[tex]t=\frac{\log_{}(\frac{n}{74})}{\log_{}(0.98)}[/tex]Step-by-step explanation:
The number of amphibians in the forest after t years can be given by an equation in the following format:
[tex]N(t)=N(0)(1-r)^t[/tex]In which N(0) is the initial number of amphibians and r is the decrease rate, as a decimal.
Decreasing by 2% per year.
This means that r = 0.02.
There are currently 74 species of amphibians in the rain forest.
This means that N(0) = 74.
So
[tex]N(t)=74(1-0.02)^t=74(0.98)^t[/tex]Which logarithmic function models the time, f(n), in years, it will take the number of species to decrease to a value of n?
This is t for which N(t) = n. So
[tex]74(0.98)^t=n[/tex][tex](0.98)^t=\frac{n}{74}[/tex][tex]\log _{}(0.98)^t=\log _{}(\frac{n}{74})[/tex][tex]t\log _{}(0.98)=\log _{}(\frac{n}{74})[/tex][tex]t=\frac{\log_{}(\frac{n}{74})}{\log_{}(0.98)}[/tex]
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