Question

A company launches 4 new products.

The market price, in dollars, of the four products after a different number of years, x, is shown in the following table:

Product 1 | f(x)=3^x |$3 | $9| $27
Product 2 | g(x)= x^2+4| $5 | $8 | $13
Product 3 |h(x)=3x+8| $11| $14| $17
Product 4 | j(x) = x^3| $1 | $8 | $27

Based on the data table, for which product does the price eventually exceed the others?

A. product 1
B. Product 2
C. Product 3
D. Product 4

Answer 1

A. product 1

Explanation:

An exponential function (with a base larger than 1) will eventually exceed the value of any polynomial function. Product 1 has a price described by an exponential function, so its price will exceed all others. (One only need to compute the values for x=4 to see this.)

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The attachment extends the table and plots the functions up to the point where Product 1 exceeds the others.