Find the formula for an exponential function that passes through the two points given. ( 0 , 7 ) and ( 4 , 16807 )

Question

Find the formula for an exponential function that passes through the two points given. and 

Answer 1

f(x) = k*B^x

f(0) = 7 ---> k = 7

f(4) = 16807 ---> 16807 = 7 * b^4

2401 = b^4

b^4 - 2401 = 0

( b^2 + 49 )( b^2 - 49 ) = 0

b^2 + 49 =0 results in imaginary/comp0lex solutions +or- 7i

b^2 - 49 results in b=7 or b=-7

So

f(x) = 7 * 7^x = 7^(x+1)