I don't even know where to begin on this problem...
The function f(x) is an unshifted exponential function which goes through the oints (2,5) (3,4).
a)What is the equation for f(x)?
b)write f(10) and f(100).
If it's an exponential function then we know f(x)=a^x. The fact that it's unshifted means there's no constant term added to it. We also know that
(1) f(2)=c*a^2=5
(2) f(3)=c*a^3=4
Divide (2) by (1) to get a=4/5
Now put that in either to solve for c, thus
c*(4/5)^2=5 and solving for c we get c=125/16
Thus f(x)=(125/16)(4/5)^x
Test the values 2 and 3 for x to make sure they work.
Do you follow all the steps I did?
I had gotten 4/5 because a friend had started to explain it to me then the bell rang and I knew how I had gottne the4/5 but I was't sure what to do with it...thanks
Yes, I follow the steps you have done so far. After finding the value of a as 4/5, you correctly substituted it back into one of the equations to solve for c. The value of c obtained was 125/16.
Now that you have determined the values of a and c, you can write the equation for f(x) as f(x) = (125/16) * (4/5)^x.
To find f(10), you can substitute x = 10 into the equation: f(10) = (125/16) * (4/5)^10. Similarly, to find f(100), substitute x = 100 into the equation: f(100) = (125/16) * (4/5)^100.
Do you have any more questions or is there anything else I can help you with?