SOLUTION: the growth of a herd of a bison follows the rule P(t) = P( base 0 )(2^(t/10) where P(base 0) represents the initial population and P(t) represents population after x years. In how

Algebra ->  Finance -> SOLUTION: the growth of a herd of a bison follows the rule P(t) = P( base 0 )(2^(t/10) where P(base 0) represents the initial population and P(t) represents population after x years. In how       Log On


   

Question 824835: the growth of a herd of a bison follows the rule P(t) = P( base 0 )(2^(t/10) where P(base 0) represents the initial population and P(t) represents population after x years. In how many years will the bison population quadruple its initial population?
Thanks in advance:)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You mean this:
P%28t%29=P%5B0%5D2%5E%28t%2F10%29;-----if this is not rendering properly, the exponent is %28t%2F10%29
The initial population's variable is said as, "P sub zero". The BASE in your function is 2.

Your question is to find x for when P(x) is 4%2AP%5B0%5D. You need to decide if you want to call the time variable, x or call it t.

We can, for scribing purposes, just say initial population is p and we want t when P%28t%29=4%2Ap.
4p=p%2A2%5E%28t%2F10%29
4=2%5E%28t%2F10%29
log%2810%2C4%29=log%2810%2C%282%5E%28t%2F10%29%29%29
log%2810%2C4%29=%28t%2F10%29log%2810%2C2%29
t%2F10=%28log%2810%2C4%29%29%2F%28log%2810%2C2%29%29
highlight%28t=10%2A%28log%2810%2C4%29%29%2F%28log%2810%2C2%29%29%29----------the computation has not been completed, so it is for you to finish.