Question

Question 2 (2 points)

y=5575.(0.65)t

a. What is the initial value?

b. What is the decay factor?

Blank 1:

Blank 2:

Answer 1

a. What is the initial value?

= 5575

b. What is the decay factor?

= 0.35 or 35%

Explanation:

Exponential Decay formula is given as

y = a(1 - r)^t

Where:

a = initial value (the amount before measuring growth or decay)

r = decay rate or decay factor (most often represented as a percentage and expressed as a decimal)

t = number of time intervals that have passed

In the question above,

y=5575.(0.65)^t

a. What is the initial value?

y = a(1 - r)^t

y=5575.(0.65)^t

Hence, a = Initial value = 5575

b. What is the decay factor?

r = decay factor

Hence

1 - r = 0.65

r = 1 - 0.65

r = 0.35

The decay factor = 0.35

We can also convert to percentage

= 0.35 × 100%

= 35%

Hence, the decay factor = 0.35 or 35%

Answer 2

a. The initial value is 5575

b. The decay factor is 0.35 or 35%

Explanation:

The decay equation is given as;

y = 5575(0.65)^t

Mathematically, a decay equation can be written in the form;

A = Ir^t

where A is the amount at a time, I

is the initial value and r represents the decay rate

a. So by comparing this with what we have, we can see that the initial value is 5575

b. We want to write the decay factor

We can rewrite the equation as;

y = 5575 (1-0.35)^t

where 0.35 = 35/100 which can be said to be 35%