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

Answer 1
Use the slope formula to find the average rate of change: #m=frac{y_2-y_1}{x_2-x_1}#
#m=frac{f(4)-f(2)}{4-2}#
To simplify this, we need to find values of #f(4)# and #f(2)#: #f(4)=2(3)^4 = 2(81)=162# #f(2)=2(3)^2=2(9)=18#
#m=frac{162-18}{2}#
#m=144/2#
#m=72#
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Answer 2

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 ).

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Answer from HIX Tutor

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.

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.

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