Question

Use the table below to find the following.m: 1 2 3 p(m):210 96.6 44.436 Initial value: 1-unit growth/decay factor: 1-unit percent change: FInd the initial value and Function: p(m)=

Answer 1

decay factor = 0.46

unit percent change = 0.54

Initial value = 456.52

Function: p(m) = 456.52(0.54)^m

Step-by-step explanation:

To find the decay factor, we need to find the proportion of two consecutive values in the table. So:

96.6/210 = 0.46

44.436/96.6 = 0.46

Since both values are equal, we can say that the decay factor is 0.46

Then, the decay factor is equal to 1 - r. Where us the unit percent change. So, we can solve for r as follows:

0.46 = 1 - r

0.46 + r = 1 - r + r

0.46 + r = 1

0.46 + r - 0.46 = 1 - 0.46

r = 0.54

Therefore, the unit percent change is 0.54

On the other hand, we can calculate the initial value dividing p(1) = 210 by the decay factor. So, the initial value P(0) is:

P(0) = 210/0.46 = 456.52

Finally, the function has the form:

p(m) = 456.52(0.46)^m

Where 456.52 is the initial value and 0.46 is the decay factor.

So, the answers are:

decay factor = 0.46

unit percent change = 0.54

Initial value = 456.52

Function: p(m) = 456.52(0.54)^m