The value of is
Explanation:
The function is given by
The function is given by
To determine the value of , let us first substitute the value of
.
Thus, we get,
Now, substituting for in the function
, we get,
Simplifying, the expression, we get,
Multiplying the term within the bracket, we have,
Thus, the value of is
Hence, the value of represents the total amount of money that Barrett earns for working x hours.
Answer:
a) see the plots below
b) f(x) is exponential; g(x) is linear (see below for explanation)
c) the function values are never equal
Step-by-step explanation:
a) a graph of the two function values is attached
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b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).
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c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.
In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.
