Find the function of the form f cax that contains the two g

Find the function of the form f = ca^x that contains the two given points: a) f(0) = 1 and f(2) = 16 b) (1, 1) and (2, 5) Find an equation of the form y = c4b log_ax whose graph contains the two given points (10, 1) and (1, 2).

Solution

f = ca^x

f(0) = 1 and f(2) = 16

two points are (0,1) and (2,16)

plugging the values in the function

1 = ca^0

c = 1

16 = ca^2

a^2 = 16

a = 4

hence, function is

f = 4^x

b) (1,1) and (2,5)

plugging the points in the function

1 = ca^1

ca = 1

5 = ca^2

dividing the two equations

ca = 1

--------------

ca^2 = 5

a = 5

c = 1/5

hence, function is

f = 1/5 (5)^x