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german
1 year ago
10

The current population of a threatened animal species is 1.6 million, but it is declining with a half-life of 20 years. How many

animals will be left in 30 years? in 65 years?
Mathematics
1 answer:
GaryK [48]1 year ago
8 0

It is given that the half-life is 20 years and the current population is 1.6 million.

It is required to find the population in 30 and 65 years, respectively.

Recall the Exponential Decay Half-Life Formula:

N=N_0\left(\frac{1}{2}\right)^{\frac{t}{h}}

Where N₀ is the current population, t is the time in years, and h is the half-life.

(a) Substitute N₀=1.6, h=20, and t=30 into the formula:

N=1.6\left(\frac{1}{2}\right)^{\frac{30}{20}}\approx0.6\text{ million}=600,000

About 600,000 animals will be left in 30 years.

(b) Substitute N₀=1.6, h=20, and t=65 into the formula:

N=1.6\left(\frac{1}{2}\right)^{\frac{30}{20}}\approx0.6\text{ million}=600,000

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