Question

question 1 (multiple choice worth 2 points)
(introduction to linear functions mc)
determine which scenario would be best modeled by a linear function
○ a culture contains 300 bacteria initially. each bacterial cell splits into two every hour. after 3 hours, there were 2,400 bacterial cells present in the culture
○ a electrician charges $80 for the service call, plus an additional $50 per hour until the electrical problem is resolved.
○ a rocket is launched from the ground, rises into the sky, and then falls back to the ground
○ a new car was sold 4 years ago for $38,000. it depreciates at an average rate of 23% in the first two years and then 9% each year after

question 2 (multiple choice worth 2 points)
(introduction to linear functions mc)
a truck rental company charges $19.99 to rent a truck for the day, plus an additional $0.99 per mile driven. the linear function for the total cost is c(x) = 0.99x + 19.99. interpret (content of the problem cut off)

Explanation:

Question 1

Step 1: Analyze Option A

Bacteria splitting into two every hour is exponential growth (each hour population doubles), so model is exponential, not linear.

Step 2: Analyze Option B

Electrician's charge: fixed $80 + $50 per hour. Let \( h \) be hours, total charge \( C = 80 + 50h \), which is linear (form \( y = mx + b \)).

Step 3: Analyze Option C

Rocket's path: rises then falls, which is a parabola (quadratic), not linear.

Step 4: Analyze Option D

Car depreciation: different rates (23% then 9%), and depreciation is exponential (percentage decrease), not linear.

Step 1: Recall linear function form \( y = mx + b \), where \( m \) is rate, \( b \) is initial value.

Step 2: In \( C(x)=0.99x + 19.99 \), \( 19.99 \) is fixed daily rental (when \( x = 0 \), no miles driven), \( 0.99 \) is cost per mile, \( x \) is miles driven, \( C(x) \) is total cost.

Answer:

B. A electrician charges $80 for the service call, plus an additional $50 per hour until the electrical problem is resolved.

Question 2 (Assuming the question is about interpreting the linear function, e.g., what \( x \) or \( 0.99 \) or \( 19.99 \) represents)

(Note: Since the question is cut off, but based on context, if it's about what \( x \) represents: \( x \) is miles driven, \( 0.99 \) is cost per mile, \( 19.99 \) is daily rental. For example, if question is "What does \( x \) represent in \( C(x)=0.99x + 19.99 \)?", answer: \( x \) represents the number of miles driven.)
(If the actual question was different, adjust accordingly. But based on given text, the linear function is \( C(x)=0.99x + 19.99 \), so: