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kogti [31]
3 years ago
6

Can someone help me with this? During a certain period of time about 2000 penguins had an annual growth rate of 19% why will the

population of penguins be after 5 years? This is exponential growth and decay
Mathematics
1 answer:
Naily [24]3 years ago
4 0

Answer:

Future amount of penguin = 4,772.70

Step-by-step explanation:

Given:

Current amount of penguin = 2,000

Growth rate r = 19% = 0.19

Number of year n = 5

Find:

Future amount of penguin

Computation:

Future amount of penguin = Current amount of penguin[1+r]ⁿ

Future amount of penguin = 2000[1+0.19]⁵

Future amount of penguin = 4,772.70

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A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}

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2 years ago
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Answer:

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