By Marcel B. Finan
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Extra resources for A Reform Approach to Business Calculus
1 A polynomial function will never involve terms where the variable occurs in a denominator, underneath a radical, as an input of either an exponential or logarithmic function. 3 Determine whether the function is a polynomial function or not: (a) f (x) = 3x4 − 4x2 + 5x − 10 (b) g(x) = x3 − ex + 3 (c) h(x) = x2 − √ 3x + x1 + 4 2 (d) i(x) = x − x − 5 (e) j(x) = x3 − 3x2 + 2x − 5 ln x − 3. Solution. (a) f (x) is a polynomial function of degree 4. (b) g(x) is not a ploynomial degree because one of the terms is an exponential function.
Since t is allowed to have √ any value then a negative a will create meaningless expressions such as a (if t = 12 ). Also, for a = 1 the function P (t) = b is called a constant function and its graph is a horizontal line. 3 Suppose you are offered a job at a starting salary of $40,000 per year. To strengthen the offer, the company promises annual raises of 6% per year for the first 10 years. Let P (t) be your salary after t years. Find a formula for P (t) and then compute your projected salary after 4 years from now.
92 mg. Recognizing an Exponential Function Defined by Data Suppose that f is a function defined by a table of values. If f is an exponential function then f can be written in the form f (x) = bax . Thus, x+n f (x+n) = babaxn = an . This says that the ratios of y values are constant for f (x) equally spaced x values. Find a formula for each case. 301 g(x) 0 2 4 6 8 Solution. 638 tion. 5a. 1)x . On the other hand, equal increments in x corresponds to equal increments in the g-values so that g(x) is linear, say g(x) = mx + b.
A Reform Approach to Business Calculus by Marcel B. Finan