Question

24w - n(w) = 933.2
24x - y = 933.2
y = 24x - 933.2
n(w) = 24w - 933.2
(f) predict the number of raisins in a box that weighs 42.4 grams. use the above function.
the predicted number is 84
(round to the nearest integer as needed.)
(g) interpret the slope of the line found in part (c).
if the number of raisins increases by 1, then the weight increases by 24 grams.
if the number of raisins decreases by 1, then the weight increases by 24 grams.
if the weight increases by 1 gram, then the number of raisins increases by 24 raisins.
if the weight decreases by 1 gram, then the number of raisins increases by 24 raisins.

Explanation:

Step1: Substitute \( w = 42.4 \) into \( N(w)=24w - 933.2 \)

\( N(42.4)=24\times42.4-933.2 \)

Step2: Calculate \( 24\times42.4 \)

\( 24\times42.4 = 1017.6 \)

Step3: Calculate \( N(42.4) \)

\( N(42.4)=1017.6-933.2=84.4\approx84 \)

The slope \(m = 24\) in the linear function \(N(w)=24w - 933.2\) represents the rate of change of the number of raisins (\(N(w)\)) with respect to the weight (\(w\)). So if the weight (\(w\)) increases by 1 gram (\(\Delta w = 1\)), then the number of raisins (\(N(w)\)) increases by \(m = 24\) (since \(\Delta N(w)=m\times\Delta w\)).

Answer:

84

For part (g), using the slope - intercept form \( y = mx + b\) (here \(N(w)=24w - 933.2\) where \(m = 24\) is the slope). The slope \(m=\frac{\Delta y}{\Delta x}\) (in our case \(\frac{\Delta N(w)}{\Delta w}\)).