Question

1. a population of bacteria starts at 800 and decreases according to $p(t) = 800(0.85)^t$ where t is time in hours. which statement is true?

a. the function increases and has a horizontal asymptote at $y = 800$
b. the function represents exponential decay with a decay rate of 15%
c. the function has a domain of all real numbers and range of $y > 800$
d. the function represents exponential growth with initial value 0.85

Explanation:

Step1: Recall exponential decay form

The standard exponential decay model is $P(t) = P_0(1-r)^t$, where $P_0$ is the initial population, $r$ is the decay rate, and $t$ is time.

Step2: Match given function to model

Given $P(t) = 800(0.85)^t$, here $1-r=0.85$, so $r=1-0.85=0.15$ (15% decay rate).

Step3: Eliminate incorrect options

• Option A: The function decreases (not increases), asymptote at $y=0$, so false.
• Option C: Range is $y>0$ (not $y>800$), so false.
• Option D: It is decay (not growth), initial value is 800, so false.

Answer:

B. The function represents exponential decay with a decay rate of 15%