How to analyze a table of values to create an exponential function?

Question

Analyze the following table depicting the ladybug population and create a function using the form f(x)=ab^x

Then, calculate the ladybug population after 1 year.

time= 0, 1, 2, 3

ladybugs= 10, 30, 90, 270

Answer 1

When time is zero, there are 10 ladybugs, so the initial amount (a) is 10.

f(x) changes by a product of 3. Notice 10x3=30, 30x3=90 and so on. So our growth factor or (b) is 3.

Therefore, our equation f(x)=ab^x is f(x)=10(3)^x

Check by making sure we match the given table of values:

f(0)= 10(3)^0= 10

f(1)= 10(3)^1= 30

f(2)= 10(3)^2= 90

f(3)= 10(3)^3= 270

Then plug in 12 for x to calculate the ladybug population at 1 year.

f(12)= 10(3)^12 = 5,314,410