Question

At sea level, earths atmosphere exerts a pressure of 1 atmosphere. Atmospheric pressure P (in atmospheres) decreases with altitude and can be modeled by P = (0.99987)a where a is the altitude (in meters) identify the initial amount, decay factor, and decay rate

Answer 1

The answers to the question are as follows

Initial a amount = 1

Decay Factor =0.99987

Decay rate = 1-0.99987 = 0.00013

Explanation:

We have the formula for exponential decay given by

`y = a(1-b)^t`

In the above we have (1+b) = Decay factor

a = Initial amount

b = rate of decay

t = time

Comparing
`y = a(1-b)^t` , with the function in the question, we have

`a(1-b)^t`≡
`0.99987^a`

Therefore, a ≡ 1,

1 + b ≡ 0.99987 and

x ≡ a

Therefore we have

Initial amount = 1

Decay/growth factor = 0.99987

But rate of decay = b = 1-(1-b) =b

Therefore Rate of Decay = 1 - 0.99987

Answer 2

Initial Amount=1

Decay Factor=0.99987

Decay Rate=0.013%

Explanation:

If P = 0.99987ᵃ

I. Initial amount

The initial amount is when a=0

P = 0.99987⁰ = 1

The Pressure at Sea Level=1

II. Decay factor

This is like the decay constant. From the model, P = 0.99987ᵃ, the decay constant/factor is 0.99987.

III. Decay Rate = 1-0.99987 = 0.00013

Expressed in Percentage = 0.013%