7. Modeling with Exponential and Logarithmic Functions
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Begin by creating a table of data pairs (x,ln y) using the given information. Then, make the scatter plot of the resulting ordered pairs.
Possible Model: y=6.34(1.42)^x
We will first create a table of data pairs (x,ln y) using the given table.
x | y | ln y |
---|---|---|
1 | 9 | 2.20 |
2 | 14 | 2.64 |
3 | 19 | 2.94 |
4 | 25 | 3.22 |
5 | 37 | 3.61 |
6 | 53 | 3.97 |
7 | 71 | 4.26 |
Next, we will plot the transformed points.
Substitute ( 1,2.20) & ( 5,3.61)
Subtract terms
Calculate quotient
Distribute 0.3525
LHS+2.20=RHS+2.20
e^(LHS)=e^(RHS)
a = e^(ln(a))
a^(m+n)=a^m*a^n
(a^m)^n=a^(m* n)
Calculate power
Multiply
Round to 2 decimal place(s)