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=9.11(1.99)^x
We will first create a table of data pairs (x,ln y) using the given table.
x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
y | 18 | 36 | 72 | 144 | 288 |
ln y | 2.89 | 3.58 | 4.28 | 4.97 | 5.66 |
Next, we will plot the transformed points.
Substitute ( 3,4.28) & ( 4,4.97)
Subtract terms
a/1=a
Distribute 0.69
LHS+4.28=RHS+4.28
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)