The equation modeling the population growth of a small town is P(1) = 30000(1.02)', where P represents the population 1 years from now. What is the approximate population change that occurs between 2 years from now and 10 years from now?

A. 5,358
B. 6,570
C. 31,212
D. 35,150
E. 36,570

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Ответ:

jordanbyrd33

25.02.2022

Mathematics

x = 0True for all x

Step-by-step explanation:

$\left(7^2\right)^x=1\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\\\left(7^2\right)^x=7^{2x}\\\\7^{2x}=1\\\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(7^{2x}\right)=\ln \left(1\right)\\\ln \left(7^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\times \log _a\left(x\right)\\\\\ln \left(7^{2x}\right)=2x\ln \left(7\right)\\$

$2x\ln \left(7\right)=\ln \left(1\right)\\\mathrm{Solve\:}\:2x\ln \left(7\right)=\ln \left(1\right):\\\\\quad x=0$

$\left(7^0\right)^x=1\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\\\left(7^0\right)^x=7^{0\times \:x}\\\\7^{0\times \:x}=1\\\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \\\\\left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\\\ln \left(7^{0\times \:x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\times \log _a\left(x\right)\\\\\ln \left(7^{0\times \:x}\right)=0\times \:x\ln \left(7\right)\\$

$0\times \:x\ln \left(7\right)=\ln \left(1\right)\\\\\mathrm{Solve\:}\:0\times \:x\ln \left(7\right)=\ln \left(1\right):\quad \\\\\mathrm{True\:for\:all}\:x$

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The equation modeling the population growth of a small town is P(1) = 30000(1.02)', where P represents the population 1 years from now. What is the approximate population change that occurs between 2 years from now and 10 years from now? A. 5,358 B. 6,570 C. 31,212 D. 35,150 E. 36,570