Question

The population (in millions) of a certain island can be approximated by the function p(x)=50(1.05)^x, where x is the number of years since 2000. in which year will the population reach 200 million? hint: an answer such as 2002.4 would represent 2002. a)2028
b)2015
c)2002
d)2066
please help

Answer 1

Answer: a)2028

Step-by-step explanation:

Given: The population (in millions) of a certain island can be approximated by the function  $p(x)=50(1.05)^x$ , where x is the number of years since 2000.

To find the year in  in which year will the population reach 200 million, substitute p(x)=200, we get

$200=50(1.05)^x\\\\\Rightarrow(1.05)^x=4$

Taking natural log on both the sides , we get

$\ln((1.05)^x=\ln(4)\\\\\Rightarrow\ x(\ln(1.05))=\ln4\\\\\Rightarrow\ x=\dfrac{\ln4}{\ln(1.05})=\dfrac{1.38629}{0.04879}\\\\\Rightarrow\ x=28.4134043861\approx28\text{ years}$

The year will be $2000+28=2028$

Hence, in 2028  the population will reach 200 million.

Answer 2

The answer is A)2028 - just took the test