Calculus 1 : Prediction Models
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Example Questions
Example Question #1 : How To Find Prediction Models
Suppose you are a banker and set up a very unique function for your interest rate over time given by
However, you find your computer incapable of calculating the interest rate at 
Undefined
To do a linear approximation, we're going to create a function
Firstly, we need to find the derivative of 
By the power rule:
The slope at 
Since this is the case, the approximate value of our interest rate will be identical to the value of the original function at x=2, which is 
1 is our final answer.
Example Question #2 : How To Find Prediction Models
Approximate the value at 
To do this, we must determine the slope of the function at 
To determine slope, we take the derivative of the function with respect to x and find its value at 
At 
To determine 
At 
Since 
Example Question #2 : Prediction Models
Determine the tangent line to 
First recall that
To find the tangent line of 
Recall that derivatives of exponential functions involving 
In our case, 
At 
To use point-slope form, we need to know the value of the original function at 
Therefore,
At 
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