EXPLANATION
The function that represents the exponential decay is as follows:
[tex]f(x)=ab^x[/tex]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.
[tex]f(x)=8b^x[/tex]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:
[tex]\frac{6}{8}=\frac{8}{8}\frac{b^1}{b^0}[/tex]Simplifying:
[tex]\frac{3}{4}=0.75=b[/tex]The value of b is 3/4:
[tex]y=8\cdot0.75^x[/tex]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:
[tex]y=8\cdot(\frac{3}{4})^x[/tex]3) After 7 weeks, the area will be represented by the following expression:
[tex]y=8\cdot(\frac{3}{4})^7[/tex]Computing the power:
[tex]y=8\cdot\frac{2187}{16384}=1.068cm^2[/tex]