Digital SAT Math:Practice Questions-Passport to advanced mathematics-Graphing exponential functions

Ans:D

Given that the number of area codes is growing over time, the graph suggests an exponential growth pattern. The general form of an exponential growth equation is:

\[
y = a(b)^x
\]

Looking at the given options, the correct form must match this pattern. The options are:
A) \( y = 1.02(3.26)^{-x} \)
B) \( y = 3.26(1.02)^{-x} \)
C) \( y = 1.02(3.26)^x \)
D) \( y = 3.26(1.02)^x \)

Since the graph shows an increasing trend, we are dealing with exponential growth, so the exponent should not have a negative sign, ruling out options A and B.

Next, we look at options C and D:
 Option C: \( y = 1.02(3.26)^x \)
 Option D: \( y = 3.26(1.02)^x \)

To decide between these, we need to check the initial value and the base of the exponent. The graph starts at a point around 3 area codes when \( x = 0 \).

 In option C, the initial value \( a = 1.02 \), which does not match our initial observation.
 In option D, the initial value \( a = 3.26 \), which is closer to the starting value seen in the graph.

Therefore, the correct equation representing this relationship is:

D) \( y = 3.26(1.02)^x \)