The following tables lists the number bacteria y in millions

The following tables lists the number bacteria y in millions after an elapsed time of x days. (#122) Find values for C and a such that f(x) = Ca^x models the data.

Solution

Given a table which is about days and number of bacteria.

Given function is f(x)=Ca^x

From the table, x=0 and y=3

y = f(x)=Ca^x

y=Ca^x

3=Ca⁰

3=C(1)

C=3

From the table, x=1 and y=6

y=Ca^x and we got C=3

6=3a¹

6=3a

2=a

a=2

Therefore, a=2 and C=3