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Consider the function g (2) = 21 log2 (2 + 1) + 85.Then complete the statements.Type the correct answer in each box. Use numeralsinstead of words. Round your answers to the nearestwhole number.The population of frogs in the secondenclosure reaches 232 frogs afterapproximately( ? )weeks.Suppose the scientist determines that thesecond frog enclosure reaches its maximumcapacity after approximately 140 weeks. Thisvalue means the maximum capacity isapproximately( ? )frogs.

Consider the function g 2 21 log2 2 1 85Then complete the statementsType the correct answer in each box Use numeralsinstead of words Round your answers to the n class=
Consider the function g 2 21 log2 2 1 85Then complete the statementsType the correct answer in each box Use numeralsinstead of words Round your answers to the n class=

Respuesta :

we have the function

[tex]g(x)=21\log_2(x+1)+85[/tex]

Part 1

we have that

For g(x)=232 frogs

Find out the value of x

substitute in the given function

[tex]\begin{gathered} 232=21\operatorname{\log}_2(x+1)+85 \\ 232-85=21\log_2(x+1) \\ 147=21\log_2(x+1) \\ \frac{147}{21}=\log_2(x+1) \\ \\ 7=\log_2(x+1) \end{gathered}[/tex]

Apply property of logarithms

[tex]\begin{gathered} 2^7=x+1 \\ x=2^7-1 \\ x=127 \end{gathered}[/tex]

therefore

The answer Part 1 is 127 weeks

Part 2

For x=140 weeks

substitute in the given function g(x)

[tex]\begin{gathered} g(x)=21\operatorname{\log}_2(140+1)+85 \\ g(x)=21\log_2(141)+85 \end{gathered}[/tex]

change the base of the logarithm

Remember that

[tex]\log_2141=\frac{\log_{10}141}{\log_{10}2}=\frac{log141}{log2}[/tex]

substitute

[tex]\begin{gathered} g(x)=21\frac{log141}{log2}+85 \\ \\ g(x)=234.93 \end{gathered}[/tex]

therefore

The answer Part 2 is 235 frogs

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