mathy helpy azn needs *gah*

[kid908]

Apparently i do not know how to get the f(x) of an exponential function with given coordinates. Can someone explain how i can by hand and not by calculator that part is pretty much under "I know how to do"

The given coordinates are (1,20) and (3,320). the arrived f(x) is 5(4)^x by calculator...so... How do i do it by hand?

[Mr Buckshot]

Start with y = a*b^x - that is what your final function looks like.
Natural log both sides to get lny = lna + xlnb
So natural log your two y-values. Find a linear function (easy to do by hand) between lny and x. Your y-intercept is lna, your slope is lnb. Those are easy to find by hand.
Do e^(lny) = e^(lna + xlnb), you get y = a*b^x

For the linear function:
When you natural log your y-values, your ordered pairs as (1, ln20) and (3, ln320). So your slope is (ln320 - ln20)/2 = (ln16)/2. Therefore lnb = (ln16)/2. 2lnb = ln16, lnb^2 = ln16, b = 4
Take one of the ordered pairs, easiest to use (1, ln20). ln20 = lna + xlnb = lna + xln4, x = 1 so ln20 = lna + ln4. By the log laws, ln20 = ln4a and therefore a = 5.

Final answer: y = 5*4^x, check with your calculator!

also, check out another forum called Art of Problem Solving, threads like these belong there, you can find me on AoPS as bryant124. Post your problems there and at least 10 nerdy users will reply with correct answers, all at the same time.