Respuesta :

Answer:

a) Initial Value = 5575

Decay factor = 0.35

Explanation:

The given expression is:

[tex]Y\text{ = 5575}\times(0.65)^t[/tex]

a) What is the initial value

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

Substituting t = 0 into the given equation:

[tex]Y\text{ = 5575}\times(0.65)^0[/tex][tex]Y=\text{ 5575 }\times\text{ 1 = 5575}[/tex]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:

[tex]Y=A(1-r)^t[/tex]

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

Comparing the above equation with the given equation shown below:

[tex]Y=5575(0.65)^t[/tex]

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