please help

Question

        Find a and b which define the exponential function 𝑓(x)=a⦁b^x with points (-1, 0.75) (0,1.5) (1,3) (2,6)?

Answer 1

f(x) = ab^x

f(1) = ab

3 = ab ⇒ 3/b = a

f(2) = ab²

6 = ab² ⇒ 6/b² = a

3/b = 6/b²

3b = 6

b =2

f(x) = a(2)^x

f(1) = a(2)¹

3 = 2a

3/2 = a

f(x) = (3/2)(2^x)

Answer 2

For this problem, you would substitute the given points into the equation and solve for a and b.

 

Points:

   x   ,   y

( -1  ,  0.75)

(  0  ,  1.5)

(  1  ,  3)

(  2  ,  6)

 

Substitute into the given equation f(x) = a•b^x  or  y = a•b^x

First point

0.75 = a•b^-1 = a/b

[remember: x^-1 = 1/x]

 

Second point

1.5 = a•b⁰ = a•1 = a

[remember: x⁰=1]

 

Third point

3 = a•b¹ = a•b

 

Fourth point

6 = a•b²

 

From above, we see the four points yield the following equations:

0.75 = a/b

1.5 = a

3 = a•b

6 = a•b²

 

The second equation shows you that a = 1.5. You can plug that value into any of the other equations to find b.

If you plug a = 1.5 into the third equation, you get:

3 = 1.5 • b

b = 2

 

Final answer: a = 1.5, b = 2

 

You can confirm the answers by substituting the values into the remaining equations.