Question

The graph shows the population of a bacteria in an experiment, measured every hour.

Which function represents the population of the bacteria after t hours?
f(t) = 10(1.4)t
f(t) = 10(2.0)t
f(t) = 14(1.4)t
f(t) = 14(2.0)t

Answer 1

A on edg

Explanation:

Just took it

Answer 2

Given the graph which shows the population of a bacteria in an experiment, measured every hour.

The graph is a graph of an exponential function.

An exponential function is given by

`f(t) = a(r)^t`
where: a is the initial value of the function when t = 0,
r is the growth/decay rate, and
t is the time elapsed.

From the graph, the initial size of the population when t = 0 is 10, thus, the value of a in the function is 10.

Also, from the graph, after 2 hours, the popolation of bacteria was 20,
i.e.

`20=10(r)^2 \\ \\ r^2=2 \\ \\ r= √(2) =1.4`

Therefore, the function representing the population of the bacteria after t hours is

`f(t)=10(1.4)^t`