Question

a forest fire has been burning for several days. the burned area, in acres, is given by the equation ( y = (4,800) cdot 2^{d} ) where ( d ) is the number of days since the area of the fire was first measured.
a. complete the table.
type the answers in the boxes below

b. look at the value of ( y = 4,800 cdot 2^{d} ) when ( d = - 1 ). what does it tell you about the area burned in this fire?
( d = - 1 ) means one day before the area of the fire was first measured
( d = - 1 ) means the area decreased by 1
( d = - 1 ) means that the equation models exponential decay

Explanation:

Step1: Substitute \(d = 0\) into \(y=4800\cdot2^{d}\)

When \(d = 0\), \(y=4800\cdot2^{0}\). Since \(a^{0}=1\) (\(a
eq0\)), then \(y = 4800\times1=4800\)

Step2: Substitute \(d = 1\) into \(y=4800\cdot2^{d}\)

When \(d = 1\), \(y=4800\cdot2^{1}\). Since \(a^{1}=a\), then \(y = 4800\times2 = 9600\)

Step3: Substitute \(d = 2\) into \(y=4800\cdot2^{d}\)

When \(d = 2\), \(y=4800\cdot2^{2}\). Since \(2^{2}=4\), then \(y=4800\times4 = 19200\)

Step4: Substitute \(d = 3\) into \(y=4800\cdot2^{d}\)

When \(d = 3\), \(y=4800\cdot2^{3}\). Since \(2^{3}=8\), then \(y=4800\times8=38400\)

Step5: Substitute \(d = 4\) into \(y=4800\cdot2^{d}\)

When \(d = 4\), \(y=4800\cdot2^{4}\). Since \(2^{4}=16\), then \(y=4800\times16 = 76800\)

The variable \(d\) represents the number of days since the area of the fire was first measured. When \(d=- 1\), it means one day before the area of the fire was first measured.

Answer:

\(d\), days since first measurement	\(y\), acres burned since fire started
\(1\)	\(9600\)
\(2\)	\(19200\)
\(3\)	\(38400\)
\(4\)	\(76800\)

For part \(b\):