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=4.48(1.16)^x
We will first create a table of data pairs (x,ln y) using the given table.
x | -8 | -5 | -2 | 1 | 4 |
---|---|---|---|---|---|
y | 1.4 | 1.67 | 5.32 | 6.41 | 7.97 |
ln y | 0.34 | 0.51 | 1.67 | 1.86 | 2.08 |
Next, we will plot the transformed points.
Substitute ( -8,0.34) & ( 4,2.08)
- (- a)=a
Add and subtract terms
Calculate quotient
Distribute 0.145
LHS+0.34=RHS+0.34
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)