Question

Y=5575•(0.65)^ta. What is the initial value? b. What is the decay factor?

Answer 1

Answer:

a) Initial Value = 5575

Decay factor = 0.35

Explanation:

The given expression is:

$Y\text{ = 5575}\times(0.65)^t$

a) What is the initial value

The initial value of Y will take place when t = 0

Substituting t = 0 into the given equation:

$Y\text{ = 5575}\times(0.65)^0$$Y=\text{ 5575 }\times\text{ 1 = 5575}$The initial value is Y = 5575

b) What is the decay factor

The value of a substance due to an exponential decay is given by the general expression:

$Y=A(1-r)^t$

Where A = original/Initial value, and r = decay rate

Comparing the above equation with the given equation shown below:

$Y=5575(0.65)^t$

It is clear from the comparison of both equations that A = 5575 and :

1 - r = 0.65Solving for r:r = 1 - 0.65r = 0.35The decay factor is 0.35