Question

In order for the table below to show exponential decay, what must the value of d be in the table below?

d =  18

Answer 1

Let x represent the domain
Let y represent the range.

Assume that y =a*b⁻ˣ

Set x=0:
a*b⁰ = 32
a = 32

Set x=1:
32*b⁻¹ = 24
32 = 24b
b = 32/24

Set x=2:
d = 32*(32/24)⁻²
   = 32*(24/32)²
   = (32*24*24)/(32*32) = 24²/32 = 576/32
   = 18

Answer: 18

Answer 2

The value of d from the exponential function as shown in the table is 18.

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

From the table, at point (0, 32):

32 = ab⁰

a = 32

Also, at point (1, 24):

24 = 32b

b = 0.75

y = 32(0.75)ˣ

At point x = 2:

d = 32(0.75)² = 18

The value of d from the exponential function as shown in the table is 18.

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