(1, 0.5 ) (4, 4) find the exponential function

Answer 1

y=ab^x

4=ab^4

.5=ab

a=1/2b

4 =(1/2b)b^x = b^3/2

b^3 =8

b = 2

a=1/2b = 1/4

y = f(x) = (1/4)(2^x)

f(x) = 0.25(2^x)

or you could also find an equation

y=b^x + c

4=b^4 + c

1/2=b + c

b=1/2 - c

b^4 = (1/2 -c)^4

subtract

b^4= 4-c to get

(1/2-c)^4 - 4+c = 0

solve for c

Answer 2

0.5 = ab¹

4 = ab⁴

8 = b³ divide second equation by first.

2 = b

0.5 = a(2)

0.25 = a

f(x) = 0.25)(2^x)