Answer:
31
Step-by-step explanation:
An exponential function in mathematics is an exponential function is a function of the form where b is a positive real number, and in which the argument x occurs as an exponent. So its a function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
Answer:
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7D)
Step-by-step explanation:
Given
![f(x) = \frac{7}{2}x - 16](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dx%20-%2016)
Required
The difference quotient for h
The difference quotient is calculated as:
![\frac{f(x + h) - f(x)}{ h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D)
Calculate f(x + h)
![f(x) = \frac{7}{2}x - 16](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dx%20-%2016)
![f(x+h) = \frac{7}{2}(x+h) - 16](https://tex.z-dn.net/?f=f%28x%2Bh%29%20%3D%20%5Cfrac%7B7%7D%7B2%7D%28x%2Bh%29%20-%2016)
![f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16](https://tex.z-dn.net/?f=f%28x%2Bh%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dx%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016)
The numerator of
is:
![f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%20%5Cfrac%7B7%7D%7B2%7Dx%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016%20-%28%5Cfrac%7B7%7D%7B2%7Dx%20-%2016%29)
![f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%20%5Cfrac%7B7%7D%7B2%7Dx%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016%20-%5Cfrac%7B7%7D%7B2%7Dx%20%2B%2016)
Collect like terms
![f(x + h) - f(x) = \frac{7}{2}x -\frac{7}{2}x + \frac{7}{2}h- 16 + 16](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%20%5Cfrac%7B7%7D%7B2%7Dx%20%20-%5Cfrac%7B7%7D%7B2%7Dx%20%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016%20%2B%2016)
![f(x + h) - f(x) = \frac{7}{2}h](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dh)
So, we have:
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7Dh%20%5Cdiv%20h)
Rewrite as:
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7Dh%20%2A%20%5Cfrac%7B1%7D%7Bh%7D)
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7D)
It will take you double the time, or 78 seconds.