Write the exponential function ( y=ab^x) that goes through the points (1,6) and (3,54)

Question

Please help I really need it and I don’t have a clue how to do this also please be accurate

Answer 1

f(x) = a(b)^x

b = 1 + r

r = growth/decay rate (decimal)

a = initial amount

1. (1,6) --> f(1) = 6 --> a*b¹ = 6
2. (3,54) --> f(3) = 54 --> a*b³=54

for 1. a = 6/b substituting the a value into 2nd equation, (6/b)*b³ =54

6b² = 54. b² = 9 b = 3

f(x) = a(3)^x

using the 1st point (1,6)

6 = a(3)¹

a = 2

so final equation: f(x) 2* 3^x