The exponential function y = 2 (3) x grows by a factor of 9 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?

Given the function y=2 (3) ^x

the growth factor between x=1 and x=3 is given by:

[2 (3) ^3]/[2 (3) ^1]

=54/6

=9

thus the growth factor between x=5 and x=7 will be as follows:

[2 (3) ^7]/[2 (3) ^5]

simplifying the above we get:

=[3^7]/[3^5]

=3^ (7-5)

=3^2

=9