Question

a group of scientists are studying how a chemical effects the growth rate of bacteria. the scientists start with a group of 100 bacteria. they check the number of bacteria after each hour and determine that the growth rate for the bacteria is 4.5%. which equation represents this exponential relationship if represents time in hours? a. $f(t) = 100(1.45)^t$ b. $f(t) = 10(1.045)^t$ c. $f(t) = 100(1.045)^t$ d. $f(t) = 10(1.45)^t$

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth model is $f(t) = P(1+r)^t$, where $P$ is the initial amount, $r$ is the growth rate (in decimal), and $t$ is time.

Step2: Identify given values

Initial bacteria $P=100$, growth rate $r=4.5\% = 0.045$.

Step3: Substitute values into formula

Substitute $P=100$ and $r=0.045$ into the formula:
$f(t) = 100(1+0.045)^t = 100(1.045)^t$

Step4: Match with options

The derived equation matches option C.

Answer:

C. $f(t) = 100(1.045)^t$