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

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:

$\frac{6}{8}=\frac{8}{8}\frac{b^1}{b^0}$

Simplifying:

$\frac{3}{4}=0.75=b$

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:

$y=8\cdot(\frac{3}{4})^x$

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

$y=8\cdot(\frac{3}{4})^7$

Computing the power:

$y=8\cdot\frac{2187}{16384}=1.068cm^2$