Question

A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown on the graph

Answer 1

Step-by-step explanation

The function that represents the exponential decay is as follows:

`f(x)=ab^x`

Where a=initial amount and b= decay coefficient

Since the initial amount is 8cm^2, the is the value of the coefficient a is 8.

`f(x)=8b^x`

Now, we need to compute the decay rate:

We can obtain this by substituting two given values, as for instance (0,8) and (1,6) and dividing them:

`(6)/(8)=(8)/(8)(b^1)/(b^0)`

Simplifying:

`(3)/(4)=0.75=b`

The value of b is 3/4:

`y=8\cdot0.75^x`

1) There will be 3/4 of the burn area each week.

2) The equation representing the area of the burn, after t weeks will be the following:

`y=8\cdot((3)/(4))^x`

3) After 7 weeks, the area will be represented by the following expression:

`y=8\cdot((3)/(4))^7`

Computing the power:

`y=8\cdot(2187)/(16384)=1.068cm^2`