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An animal reserve has 20,000 elk. The
population is increasing at a rate of 8% per
year. There is a concern that the food will be
scarce when the population doubles. How
long will it take for the population to reach
40,000. Show and explain your work.

An animal reserve has 20000 elk The population is increasing at a rate of 8 per year There is a concern that the food will be scarce when the population doubles class=

Respuesta :

ferrybukantoro

Answer:

9 years

Step-by-step explanation:

by using the formula :

20,000(1 + 0.08) ^n = 40,000

=> (1.08)^n = 40,000/20, 000

(1.08) ^n = 2

n = 9

[tex]\\ \rm\Rrightarrow P(1+r)^n=I[/tex]

  • P is principal
  • R is rate if interest
  • I is final amount

[tex]\\ \rm\Rrightarrow 20000(1+0.08)^n=40000[/tex]

[tex]\\ \rm\Rrightarrow (1.08)^n=2[/tex]

[tex]\\ \rm\Rrightarrow log(1.08)^n=log2[/tex]

[tex]\\ \rm\Rrightarrow nlog1.08=log2[/tex]

[tex]\\ \rm\Rrightarrow n(0.033)=0.3[/tex]

[tex]\\ \rm\Rrightarrow n=3(3)=9[/tex]

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