# Thread: problem solving on function!

1. ## problem solving on function!

Pollution control has become a very important concern in all countries. If controls are not put in place, it has been predicted that the function P=10000t^5/4 + 14000 will describe the average pollution, in particles of pollution per cubic centimeter, in most cities at time t, in years,where t=0 corresponds to 1970 and t=37 correspond to 2007. Predict the pollution for 2007, 2010 and 2020.

Any idea would be helpful at this point!!! Thanks!

2. Well first we need to find out what those years represent in terms of t:

So:
$\displaystyle 2007 - 1970 = 37 = t_1$
$\displaystyle 2010 - 1970 = 40 = t_2$
$\displaystyle 2020 - 1970 = 50 = t_3$

Then we substitute these back into the equation given for the pollution:

$\displaystyle P=10000(37)^{5/4} + 14000 = ?$
$\displaystyle P=10000(40)^{5/4} + 14000 = ?$
$\displaystyle P=10000(50)^{5/4} + 14000 = ?$

See how those numbers come out.

3. Originally Posted by lolalovepink
Pollution control has become a very important concern in all countries. If controls are not put in place, it has been predicted that the function P=10000t^5/4 + 14000 will describe the average pollution, in particles of pollution per cubic centimeter, in most cities at time t, in years,where t=0 corresponds to 1970 and t=37 correspond to 2007. Predict the pollution for 2007, 2010 and 2020.

Any idea would be helpful at this point!!! Thanks!
This is a problem of simply plugging in values (substitution).

If the function is $\displaystyle P=10000\cdot t^{5/4} + 14000$ and if 2007 is represented by t=37 (because the function models the population of 1970 when t=0), then we simply must replace the t in the function with 37:

$\displaystyle P=10000\cdot37^{5/4} + 14000$

Just do the math out, and we get $\displaystyle P=926541$ (I think, I'm not sure if you mean $\displaystyle t^{5/4}$ or $\displaystyle \frac {10000t^5}{4}$)

If t =0 in 1970, then if we want to calculate to population for 2010, we simply find the difference between 2010 and 1970, which is 40 years. So t= 40

Plug in the number: $\displaystyle P=10000\cdot40^{5/4} + 14000$ and solve. I think you can figure out the last one.