Question

Scientists are studying a bacteria sample. The function

f(x)=245(1.12)* gives the number of bacteria in the sample at
the end of x days.
Which statement is the best interpretation of one of the values in
this function?
• The initial number of bacteria is 12.
The number of bacteria at the end of one day is 245.
The initial number of bacteria decreases at a rate of
88% each day.
The number of bacteria increases at a rate of 12% each
day.​

Answer 1

The number of bacteria increases at a rate of 12% each

day.​

Explanation:

-This is an exponential growth/decay function of the form:

`y=ab^x, \ \ \ b=(1+r)`

Where

• b is the growth factor
• r is the growth rate
• y is the size at time x
• x is time
• a is the initial size

-Given that b>1, this is a growth function and the population increases by 12% for each unit time elapsed.

-Hence, the correct statement is the number of bacteria increases at a rate of 12% each day.​