# What is the average rate of change of the function #f(x)=2(3)^x# from x=2 to x=4?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the average rate of change of the function ( f(x) = 2 \cdot 3^x ) from ( x = 2 ) to ( x = 4 ), we first need to find the values of the function at ( x = 2 ) and ( x = 4 ).

( f(2) = 2 \cdot 3^2 = 2 \cdot 9 = 18 )

( f(4) = 2 \cdot 3^4 = 2 \cdot 81 = 162 )

Next, we calculate the change in ( f(x) ) over the interval ( x = 2 ) to ( x = 4 ):

( \text{Change in } f(x) = f(4) - f(2) = 162 - 18 = 144 )

Finally, we divide the change in ( f(x) ) by the change in ( x ) to find the average rate of change:

( \text{Average rate of change} = \frac{{\text{Change in } f(x)}}{{\text{Change in } x}} = \frac{{144}}{{4 - 2}} = \frac{{144}}{{2}} = 72 )

So, the average rate of change of the function ( f(x) = 2 \cdot 3^x ) from ( x = 2 ) to ( x = 4 ) is ( 72 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the equation of the tangent line of #f(x)=ln(x+3)/x+7x# at #x=3#?
- How do you find the points where the graph of the function #x^2+7y^2-4x-2=0# has horizontal tangents?
- How do you find the slope of a tangent line to the graph of the function #y=e^- x/(x+1)#, at x=1?
- How do you find the tangent equation of #f(x) = (sqrt(x) + 1)/(sqrt(x) + 2)# at a point with x=4?
- How do you find the average rate of change of #f(x) = 4x^3 - 8x^2 - 3# from -5 to 2?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7