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
a
Table:
B
b
Type of Function: Exponential
C
c
Function: b=12(3)^t
D
d
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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.
