Question

Given the following table, write the equation to represent the exponential function.

x y

-1 -4

0 -2

1 -1

2 -0.5

Answer 1

y = -2·(1/2)^x

Explanation:

The ratio of one table entry to the one before is ...

(-2)/(-4) = 1/2

so this is the growth factor.

The multiplier is the value of y when x=0, which is -2. So, the equation is ...

y = (multiplier)·(growth factor)^x

y = -2·(1/2)^x

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This can also be written using a negative exponent:

y = -2·2^(-x)