Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Kaylee needed to write the equation of an exponential function from points on the graph of the function. To determine the value of b, Kaylee chose the ordered pairs (1, 6) and (3, 48) and divided 48 by 6. She determined that the value of b was 8. What error did Kaylee make? Complete the explanation.

Kaylee Needed To Write The Equation Of An Exponential Function From Points On The Graph Of The Function To Determine The Value Of B Kaylee Chose The Ordered Pai class=

Sagot :

mhanifa

Answer:

  • 1

Step-by-step explanation:

The exponent function is:

  • f(x) = a*bˣ

You can find the value of b if you divide the consecutive values of f(x).

  • f(x + 1) = a*bˣ⁺¹
  • f(x + 1)/f(x) = a*bˣ⁺¹/a*bˣ = bˣ⁺¹⁻ˣ = b

The missing number in the explanation is 1.

Kaylee gets:

  • f(3) / f(1) = 48/6 = 8 but it is the value of b² not b.
semsee45

Answer:

One

Step-by-step explanation:

General form of an exponential function: [tex]y=ab^x[/tex]

where a is the initial value, b is the growth/decay factor, and x is the independent variable

If b > 1 the function will grow (increase).  If 0 < b < 1 then the function will decay (decrease)

The value Kaylee found is not the constant ratio of successive values.  She should use ordered pairs with x-values that differ by 1

This is how Kaylee computed the value of b, which was incorrect as the solution of 8 is for [tex]b^2[/tex]:

at (1, 6):   [tex]ab^1=6[/tex]

at (3, 48)  [tex]ab^3=48[/tex]

[tex]\implies \dfrac{ab^3}{ab^1}=\dfrac{48}{6}\\\\\implies b^2=8\\\\\implies b=\pm\sqrt{8} =2\sqrt{2}[/tex]

(b is positive since the function is increasing)

However, if Kaylee used the ordered pairs with a difference of one, e.g.  x = 1 and x = 2, then she would have computed the correct value of b:

at (1, 6):   [tex]ab^1=6[/tex]

at x = 2:  [tex]ab^2=y[/tex]

[tex]\implies \dfrac{ab^2}{ab^1}=\dfrac{y}{6}\\\\\implies b=\dfrac{y}{6}[/tex]

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.