
Concept explainers
Which kinds of model best describe the data and then write an equation for the function

Answer to Problem 22PPS
The given data represents a exponential model
The equation is y=3(4)x
Explanation of Solution
Given:
Concept Used:
If first difference of y-values is equal, then model be linear
If second difference be equal, then the model be quadratic
If first and second differences are not equal then the model will be exponential
Calculation:
In order to check whether the given data is linear, quadratic or exponential, find the first difference as shown below:
First differences:d=y2−y1=3−0.75=2.25d=y3−y2=12−3=9d=y4−y3=48−12d=36Second differences:d=9−2.25d=6.75d=36−9d=27Ratio of y-values:r1=a2a1=30.75=4r2=a3a2=123=4
Thus, the first difference of y-values is not equal but the second difference is also no equal , so the given data represents a exponential model
General equation of exponential function is given by y=abx the ratio is 4 so b=4
To find the value of a we use a ordered pair from the table
(0,3)y=abx3=a(4)03=a×13=a⇒a=3
Thus, the equation is y=3(4)x
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