find a formula that satisfies

Question

Find a formula for the exponential function that satisfies 𝑓(0)=6 and 𝑓(1)=42

Answer 1

6 = ab^0 + c = a + c

42 = ab^1 +c = ab+c

6=a + c, c = 6-a

42 = ab + c = ab+ 6-a = (b-1)a + 6

(b-1)a = 42-6 = 36

let a = 1, then

b-1 = 36

b= 37 and c=6-1 = 5

f(x) = 37^x + 5

f(0) = 37^0 + 5 = 1+5 = 6

f(1) = 37^1 + 5 = 37+5 = 42

f(x) = 37^x + 5 is one solution among an infinite number of exponential functions