Mrs. Long keeps 25 books on her shelf for her students to read. Six of the books are non-fiction.
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Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval
is given by
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
is given by
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
is given by
Therefore, the exponential grows at the same rate as the quadratic in the interval <span>.</span>
The rate of change of a function f(x) over an interval
is given by
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
is given by
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
is given by
Therefore, the exponential grows at the same rate as the quadratic in the interval <span>
Answer:
(a)
(b)
Step-by-step explanation:
Alphaville's Budget Surplus Model is
Betaville's Budget Surplus Model is
We want to determine the expression that shows how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue.
- To do this, we subtract Betaville's Model from Alphaville's model.
Opening the brackets
Collect like terms and simplify
The expression that shows how much greater Alphaville's Budget is:
(b) If the tax revenue that year in each town is $75,000
We want to evaluate the expression derived above when the tax revenue that year in each town is $75,000 i.e.at x=75000