To analyze the function \( f(c) = 6.85 + 2.95c \):
a. Y-Intercept
The y-intercept of a function in the form \( f(c) = mx + b \) is the value of \( f(c) \) when \( c = 0 \).
In this case, the y-intercept is:
\[ f(0) = 6.85 + 2.95(0) = 6.85 \]
Meaning: The y-intercept represents the base cost for Mrs. Franklin to go to the buffet without taking any grandchildren. This cost of $6.85 could be interpreted as a fixed charge or entry fee for one person (Mrs. Franklin herself).
b. Slope
The slope of the function is the coefficient of \( c \), which in this case is \( 2.95 \).
Meaning: The slope represents the additional cost incurred for each grandchild that Mrs. Franklin takes to the buffet. Specifically, $2.95 is the cost per grandchild.
c. Determine the number of grandchildren
If Mrs. Franklin paid $18.65 for the buffet, we need to find \( c \) such that:
\[ f(c) = 18.65 \]
Substituting \( f(c) = 6.85 + 2.95c \) into the equation, we have:
\[ 6.85 + 2.95c = 18.65 \]
To solve for \( c \), we first subtract \( 6.85 \) from both sides:
\[ 2.95c = 18.65 - 6.85 \] \[ 2.95c = 11.80 \]
Next, divide both sides by \( 2.95 \):
\[ c = \frac{11.80}{2.95} \approx 4 \]
Conclusion: Mrs. Franklin took approximately 4 of her grandchildren to the buffet.
2 answers