For the graphed function f(x) = (4)^(x - 1)+ 2, calculate the average rate of change from x = 2 to x = 4
-68
-30
68
30
Which logarithmic graph can be used to approximate the value of y in the equation 4y = 8?
To calculate the average rate of change for the function f(x) = (4)^(x - 1) + 2 from x = 2 to x = 4, we need to find the difference in the function's values at x = 4 and x = 2, and then divide it by the difference in x-values.
Step 1: Calculate f(4)
Plug x = 4 into the function:
f(4) = (4)^(4 - 1) + 2
= (4)^3 + 2
= 64 + 2
= 66
Step 2: Calculate f(2)
Plug x = 2 into the function:
f(2) = (4)^(2 - 1) + 2
= (4)^1 + 2
= 4 + 2
= 6
Step 3: Calculate the difference in f(x) values
Difference in f(x) = f(4) - f(2)
= 66 - 6
= 60
Step 4: Calculate the difference in x-values
Difference in x = 4 - 2 = 2
Step 5: Calculate the average rate of change
Average rate of change = Difference in f(x) / Difference in x
= 60 / 2
= 30
Hence, the average rate of change from x = 2 to x = 4 is 30.
For the second question, the logarithmic graph that can be used to approximate the value of y in the equation 4y = 8 is the logarithm base 4. This is because the base of the logarithm must be the same as the base in the equation. In this case, both the base of the logarithm and the base in the equation are 4.
To calculate the average rate of change of a function, you need to find the difference in function values between two given points and divide it by the difference in the x-values.
In this case, you are given the function f(x) = (4)^(x - 1) + 2 and asked to find the average rate of change from x = 2 to x = 4.
1. Substitute x = 2 into the function to find the value of f(2).
f(2) = (4)^(2 - 1) + 2 = 4 + 2 = 6
2. Substitute x = 4 into the function to find the value of f(4).
f(4) = (4)^(4 - 1) + 2 = 64 + 2 = 66
3. Calculate the difference in function values: f(4) - f(2) = 66 - 6 = 60.
4. Calculate the difference in x-values: 4 - 2 = 2.
5. Divide the difference in function values by the difference in x-values to find the average rate of change:
Average rate of change = 60/2 = 30.
Therefore, the correct answer is 30.
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To approximate the value of y in the equation 4y = 8 using a logarithmic graph, you need to rearrange the equation.
1. Start with the equation 4y = 8.
2. Divide both sides by 4 to isolate y: y = 8/4.
3. Simplify the right side: y = 2.
The equation becomes y = 2, which means the value of y is 2.
The logarithmic graph that represents this equation is a horizontal line passing through the point (0, 2) on the y-axis.
Therefore, the correct answer is a horizontal line passing through the point (0, 2) on the y-axis.