The population of deer in a certain national park can be approximated by the function p(x)=150(1.07)^x , where x is the number of years since 1995. In which year will the population reach 300? Hint: An answer such as 2002.4 would represent the year 2002.

Question

The population of deer in a certain national park can be approximated by the function p(x)=150(1.07)^x  , where x is the number of years since 1995. In which year will the population reach 300? Hint: An answer such as 2002.4 would represent the year 2002.

anonymous · Answer

Put in 300 for p(x)

300=50(1.03)^x

now just solve for x, know how to start?

anonymous · Answer

Kind of, but I in the equation wrong my bad, 300 = 150(1.07)^x

Do we start off by dividing both sides by 150?

anonymous · Answer

Yep that would be a great start

anonymous · Answer

so that would leave me with 150 = (1.07)^x
What would I do from there?

anonymous · Answer

I mean 2 = (1.07)^x

anonymous · Answer

Yep, now remember you can use logarithms to get that x out of the exponent by doing this:

$$\log _{1.07}2=\log _{1.07}1.07^{x}$$

the logarithm and base of exponent cancel on the right leaving

$$\log _{1.07}2=x$$

anonymous · Answer

Oh yeah!Now do you write it in the exponential form?

anonymous · Answer

Well ya put that bad boy in a calculator and it gives you 10.2448

so 10 years since 1995=what year?

anonymous · Answer

2005?

anonymous · Answer

Thats right

anonymous · Answer

Thanks a lot!

anonymous · Answer

You're very welcome