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.

Explanation:

Step1: Analyze Option A

Bacterial growth where each cell splits into two every hour is exponential growth (formula \( y = a \cdot r^t \), here \( a = 300 \), \( r = 2 \)), not linear.

Step2: Analyze Option B

The electrician's charge: Let \( h \) be hours, total charge \( C = 80 + 50h \). This is a linear function (form \( y = mx + b \), \( m = 50 \), \( b = 80 \)).

Step3: Analyze Option C

A rocket's path (rise then fall) is a parabola (quadratic function, due to gravity), not linear.

Step4: Analyze Option D

Car depreciation with different rates (23% then 9%) is a piece - wise exponential decay, not linear.

Answer:

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