Question

1. which statement represents a constant rate of change?

the number of bacteria in a petri dish triples every hour.
you are making meatballs. it takes you 30 minutes to make 30 meatballs and then another 20 minutes to make the remaining 30 meatballs.
an electrician earns $50 the first hour plus $35 for every additional hour.
the money you deposit in the bank earns 2% interest. this means that the bank pays you 2% of the amount of the balance in the account each year.

Explanation:

• For the bacteria in a petri dish: The rate of change is not constant. If it triples every hour, the growth is exponential. For example, if there are \(x\) bacteria initially, after 1 hour there are \(3x\), after 2 hours \(9x\). The change from hour 1 to 2 is \(9x - 3x=6x\), and from 0 to 1 is \(3x - x = 2x\). Different changes over equal time intervals.
• For making meatballs: First, the rate for the first 30 meat - balls is \(\frac{30\ meat - balls}{30\ minutes}=1\ meat - ball\ per\ minute\). For the second 30 meat - balls, the rate is \(\frac{30\ meat - balls}{20\ minutes}=1.5\ meat - balls\ per\ minute\). Different rates.
• For the electrician: Let \(x\) be the number of additional hours. The total earnings \(y\) can be modeled by the linear equation \(y = 50+35x\). The slope of this linear equation is 35, which represents the rate of change of earnings with respect to the number of additional hours. For each additional hour (\(\Delta x = 1\)), the earnings change by \(\Delta y=35\).
• For the bank deposit: The interest is compound (assuming it's compound interest, even if simple - interest is considered \(I = Prt\), but when the balance changes, the interest amount changes). If the balance is \(B\), the interest in the first year is \(0.02B\), and if the balance becomes \(B + 0.02B=1.02B\) in the second year, the interest is \(0.02\times(1.02B)\). The rate of change of the total amount (principal + interest) with respect to time is not constant.

Answer:

An electrician earns $50 the first hour plus $35 for every additional hour.