Question

multiple choice 10 points. a scientist is studying a population of bacteria. she uses the function ( a(x)=785(0.38)^x ) to represent the number of bacteria over time. which statement is the best interpretation of this function? a the initial number of bacteria decreases at a rate of 38% each day. b the initial number of bacteria increases at a rate of 62% each day. c the initial number of bacteria increases at a rate of 38% each day. d the initial number of bacteria decreases at a rate of 62% each day.

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - decay function is $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time. In the given function $A(x)=785(0.38)^x$, we can rewrite $0.38$ as $1 - 0.62$.

Step2: Identify the rate of change

Here, $a = 785$ (the initial number of bacteria), and since $0.38=1 - 0.62$, the rate of decay $r = 0.62$ or $62\%$. This means the initial number of bacteria decreases at a rate of $62\%$ each day.

Answer:

D. The initial number of bacteria decreases at a rate of 62% each day.