MATH W HELP NEEDED

Question

Find a formula for the exponential function passing through the points (-3,5/8) and (1,10)

y =   

Answer 1

1) 10 = ab¹

2) 5/8 = ab^-3

3) 16 = b⁴, divide 1) by 2)

±2 = b

10 = a(±2)

±5 = a

Either a and b are positive or a and b are negative.

f(x) = 5(2)^x, or f(x) = -5(-2)^x

Answer 2

exponential function passing through points (-3,5/8) and (1,10)

y = ab^x

10 = ab^1 = ab

a =10/b

5/8 = ab^-3 = a/b^3 = (10/b)/b^3 = 10/b^4

b^4 = 80/5 = 16

b^2 =4

b = 2

a = 10/2 = 5

f(x) = 5(2^x) is the exponential function through the two given points

check the answer

10=5(2^1)

5/8 = 5(2^-3)= 5/8

(note: b^4=16 has 4 solutions. 2,-2,2i, -2i. 1 positive, 1 negative and 2 imaginary. Usually the solution you want is the positive with a continuous standard graph, especially when the problem asks for a "function." the other 3 graphically are discontinuous and not functions, but relaations of separate points)