Question 204458: Time (h) 0, 8, 16, 24, 32, 40, 48
Amount (g) 4.84, 4.63, 4.52, 4.45, 4.33, 4.19, 4.08
(a) Find an appropriate exponential model of the data points.
Amount at time t, A(t) =
I know I have to make two equations y=Ca^x
would someone be able to explain the steps please?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Time (h) 0, 8, 16, 24, 32, 40, 48
Amount (g) 4.84, 4.63, 4.52, 4.45, 4.33, 4.19, 4.08
(a) Find an appropriate exponential model of the data points.
Amount at time t, A(t) =
-----------------------
Pick any two points like (8,4.63) and (16,4.52)
Substitute those value into A(t) = a*b^x
4.52 = a*b^16
4.63 = a*b^8
-----
Divide the equation with the lower power into the one with the higher power
to get rid of "a" and to solve for "b":
You get b^8 = 0.9762
Therefore b = 0.9970
----------------------------
Substitute a known b-value into either equation to solve for "a":
4.63 = a*b^8
4.63 = a*0.9762
a = 4.7429
---------
Equation:
A(t) = 4.7429*(0.9970)^x
==================================
Comment: I could have made this easier if I had chosen the
point with x=0 but I wanted to illustrate the general
procedure.
If you calculate the A(t) values using the equation you will
see that they differ slightly from the data you were given.
That is because I rounded off the values of both a and b.
======================================
Cheers,
Stan H.
|
|
|
