Question

question 10 of 25
in a medical experiment, the number of bacteria is halved every hour. what type of function represents this pattern?

a. increasing linear

b. exponential decay

c. decreasing linear

d. exponential growth

Explanation:

1. Analyze linear functions: Linear functions have a constant rate of change (slope). For a linear function, the change in the quantity is constant per unit time. Here, the number of bacteria is halved every hour, so the rate of change is not constant (e.g., if starting with 100, after 1 hour it's 50 (change of -50), after 2 hours it's 25 (change of -25) – the change is not constant), so it's not linear (eliminates A and C).
2. Analyze exponential functions: Exponential functions have the form \( y = a(b)^x \), where \( b \) is the growth/decay factor. If \( 0 < b < 1 \), it's decay; if \( b>1 \), it's growth. Here, the number of bacteria is halved every hour, so the decay factor \( b=\frac{1}{2} \) (which is between 0 and 1), so it's exponential decay (eliminates D as growth would have \( b > 1 \)).

Answer:

B. Exponential decay