anonymous
  • anonymous
HELP PLEASE!!! The population (in millions) of a certain country can be approximated by the function P(x)=50(1.03)^x, where x is the number of years since 2000. In which year will the population reach 100 million? Hint: An answer such as 2002.4 would represent the year 2002.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
can I just guess and check for "x" untill I get 100,000,000?
anonymous
  • anonymous
You could just guess and check. But there is a way for solving equations with the variable being a exponent. It requires the use of logarithms. You have \(P(x)=50(1.03)^x\) and you know that \(P(x)=100\). So you have the equation \[100=50(1.03)^x\] You need to solve for \(x\). So the process is: \[\eqalign{ &100=50(1.03)^x \\ &2=(1.03)^x \\ &log_{10}(2)=x\phantom{.}log_{10}(1.03) \\ & \\ &\frac{log_{10}(2)}{log_{10}(1.03)}=x \\ &x\phantom{.}\dot{=}\phantom{.}23.45\phantom{.}\dot{=}\phantom{.}23 }\]
anonymous
  • anonymous
To prove it: \[P(23.45)=50(1.03)^{23.45}\dot{=}50(2.0000134641)\dot{=}100\]

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anonymous
  • anonymous
I realize now why I was so confused because I forgot to appropriately put the 100 million in decimal form, thank you Keith!
anonymous
  • anonymous
Anytime chowbelly!

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