Question

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

A graph shows time (hours) labeled 1 to 10 on the horizontal axis and population on the vertical axis. A line increases from 0 to 6.

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

f(t) = 10(1.4)^t

Reason: the graph shows an initial population of 10 and after 1 hour the population is 14, so the hourly growth factor is 14/10 = 1.4. Thus f(t)=10(1.4)^t.