a If the first and second differences are not equal, find the ratios between the successive y-values.
B
b In Part A, we determined the type. Use the general form of that type.
C
c Use the function in Part B.
A
aType of Function: Exponential
B
b y=10(2)^x
C
c 640
a To determine the type of function best models data, we will first find the first differences. If they are not equal, we will find the second differences.
We see that neither the first differences nor the second differences are equal. Hence, the table represents neither a linear nor a quadratic function. Now, we will check if there is a constant ratio between the successive y-values.
We see that there is constant ratio of 2 between each consecutive terms. Therefore, an exponential function models the data.
b We can model the number y of car club members after x years by using the general form of an exponential function.
y=a(b)^x
Here, a is the initial value and b is the constant multiplier. Then, a=10 and b=2
y=a(b)^x ⇔ y=10(2)^x
c We will use the function we wrote in Part B to predict the number of car club members after 6 years.
