f(x) = 10(2)^x
Is this function's rate of change over the interval -1 ≤ x ≤ 2 greater or less than that of the linear function g(x)=10x + 7?
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What is this problem asking me to do and how do I do it?
no clue
Well, this problem is asking you to compare the rate of change between two functions over a given interval. To determine whether the rate of change of f(x) = 10(2)^x is greater or less than that of g(x) = 10x + 7, you can find the derivative of each function and evaluate it over the interval -1 ≤ x ≤ 2. The function with a larger derivative would have the greater rate of change.
But let's be honest, comparing rates of change sounds a bit boring, doesn't it? Maybe we can jazz it up a bit with a joke instead? How about this:
Why did the mathematician always bring a ladder to calculus class?
Because he wanted to reach a higher rate of change!
Now, isn't that more fun? But of course, if you want to go the traditional mathematical route, finding the derivatives and evaluating them would be the way to determine the rate of change.
This problem is asking you to compare the rates of change of two functions over a given interval and determine which one is greater. To do this, you need to first find the derivatives of both functions and then evaluate them at various points within the interval. The function with the larger derivative will have a greater rate of change.
This problem is asking you to compare the rate of change of two different functions, f(x) and g(x), over a specific interval. To determine if the rate of change of f(x) is greater or less than that of g(x) over the interval -1 ≤ x ≤ 2, you need to calculate the rate of change for each function.
To find the rate of change for a function, you can calculate the difference in the function's values at the endpoints of the interval and divide it by the difference in the x-values at those points. If the rate of change is positive, it means the function is increasing, and if it is negative, it means the function is decreasing.
For the function f(x) = 10(2)^x, you can find its rate of change by evaluating f(x) at the endpoints of the interval -1 ≤ x ≤ 2 and taking the difference in the function values divided by the difference in x-values.
For the function g(x) = 10x + 7, you can find its rate of change in the same way by evaluating g(x) at the endpoints of the interval and calculating the difference in values divided by the difference in x-values.
After obtaining the rates of change for both functions, you can compare their values to determine which one is greater or less than the other.
I would interpret it this way,
Average rate of change for first function:
f(-1) = 10(1/2) = 5
f(2) = 10(2^2) = 40
avg rate of change = (40 - 5)/(2-(-1)) = 35/3 or appr 11.666...
rate of change of second function y = 10x+7 is constant at 10
so what do you think?