Question

Study the pattern in each table. Tell whether the relationship between X and Y is linear, inverse, exponential, or neither, and explain your reasoning. If the relationship is linear, inverse, or exponential, write an equation for it.

I need help with 6-9. Please help me.

Answer 1

6. y = 2·2^x — exponential

7. y = (1/16)·4^x — exponential

8. neither

9. neither

Explanation:

First of all, no table with an entry for 0 will be an inverse relation. When the ratio of one term to the next is a constant, the function is exponential. When the difference from one term to the next is a constant, the function is linear.

Here, some tricks are thrown in. The first two (6 and 7) are exponential functions. The common ratios are 2 and 4, respectively. The multiplier is the value of the function when x=0.

6. y = 2·2^x

7. y = (1/16)·4^x

8. The table for function 8 is that of what is known as a harmonic sequence. The denominator increases linearly. It is a kind of an inverse function, but not the kind we normally call an inverse function.

y = 1/(x+1)

9. The function is not obviously linear, inverse, or exponential. The 6 points can always be described by a polynomial of degree n-1, where n is the number of points. The 5th-degree polynomial that fits these points is tedious to find, but can be found to be ...

y = (120 + 103702x - 213975x^2 + 149665x^3 - 42225 x^4 + 4393x^5)/120

Since the function is not of one of the kinds listed, you are under no obligation to write an equation for it.