a To find the next number, multiply the previous number by 3.
B
b Consider the table you made in Part A. Find a pattern using successive differences or ratios.
C
c To write the function, use the general form of the function you found in Part B.
D
d Substitute the given value into the equation you found in Part C.
A
aTable:
B
bType of Function: Exponential
C
cFunction: b=12(3)^t
D
d 78 732
Practice makes perfect
a We know that a bacteria culture triples every hour and initially there are 12 bacteria. Let's make a table to show the bacteria population for the first 4 hours.
b From the table in Part A, we see that there is constant ratio (3) between each consecutive terms. Therefore, an exponential function models the data.
c We can model the amount of bacteria b after t hours by the exponential function below. b=a(c)^t In this form, a is the initial value and c is the constant multiplier. Then, a=12 and c=3
b=a(c)^x ⇔ b=12(3)^t
d To find the bacteria population after 8 hours, we will substitute 8 for t into the equation.
