Find an equation of the form f(x)=ab^x for the function.

Question

The ordered pairs (0, 0.5) and (1, 2) satisfy an exponential growth function. Find an equation of the form f(x)=ab^x for the function.

Enter the correct value in the box.

Answer 1

Answer 0.5* 4^x

Step 1: Points given (0,0.5) and (1,2)

Step 2: We know f(0) = 0.5 and f(1) = 2. This is another way of writing what's given in step 1

Step 3: We are given 0.5 = a*b⁰ and 2 = a*b¹ Using information from step 1 and step 2.

*Note rule b⁰= 1

*Note rule b¹=b

So 0.5 = a*(1) = a

2 = a*b = ab

Step 4: Since we know a=.5 we can use it to solve for b

2 = 0.5*b

2/.05 =b

b=4

Step 5: we know a and b.

f(x) = 0.5 * 4^x

Answer 2

f(x) = a • b^x Need to find values for a and b by using the two ordered pairs provided.

For (0, 0.5): 0.5 = a • b⁰ but b⁰ = 1, so a = 0.5. Use that for the 2nd pair.

For (1, 2): 2 = 0.5 • b¹ but b¹ = b, so b = 2/0.5 = 4

The function is f(x) = 0.5 • 4^x You can check by inserting the values for the ordered pairs into the function. where f(x) = y, x = x.

For (0, 0.5): 0.5 = 0.5 • 4⁰ (OK)

For (1, 2): 2 = 0.5 • 4¹ (OK)

Don't know what value they want you to place in the box.