Question

b. look at the value of ( y = 4,800cdot2^{d} ) when ( d=-1 ). what does it tell you about the area burned in the 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 this situation models exponential decay
( d=-1 ) means one day after the area of the fire was first measured
c. how much area had the fire burned a week before it measured 4,800 acres?
type the answer in the box below

Explanation:

Step1: Analyze the meaning of \(d\)

In the context of measuring the area burned over time, \(d = 0\) likely represents the day when the area was first measured. A negative value of \(d\) would then represent days before that initial measurement. So, \(d=-1\) means one day before the area of the fire was first measured.

Step2: Analyze other options

• Option 2: \(d=-1\) is not about the area decreasing by 1. The formula \(y = 4800\cdot2^{d}\) is about growth/decay over days, not a simple subtraction of 1 from the area.
• Option 3: The fact that \(d = - 1\) doesn't directly tell us about the type of model (exponential decay or growth). The form \(y=a\cdot b^{d}\) with \(b>1\) (here \(b = 2\)) is exponential growth.
• Option 4: A positive \(d\) would represent days after the initial measurement.

Step3: Calculate the area a week before (\(d=-7\))

We use the formula \(y = 4800\cdot2^{d}\). Substitute \(d=-7\) into the formula:

$$y=4800\cdot2^{-7}$$

$$y = 4800\times\frac{1}{2^{7}}$$

$$y=\frac{4800}{128}$$

$$y = 37.5$$

Answer:

b. \(d=-1\) means one day before the area of the fire was first measured.
c. \(37.5\)