Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which exponential function passes through the points (0’21)and (1’3)

Sagot :

Answer:

[tex]y=21\left(\dfrac{1}{7}\right)^x[/tex]

Step-by-step explanation:

Exponential Equations

Exponential functions or equations are expressions that show either exponential growth or decay and have the format of,

                                                 [tex]y=a(b)^x[/tex],

where a is the y-intercept, b is the growth/decay factor (if it's growth then, b > 1; if it's decay then, 0 < b < 1).

[tex]\hrulefill[/tex]

Solving the Problem

Algebraic Solution:

We're given two solutions to our mystery exponential function: (0, 21) and (1, 3). We can plug them into the general formula and solve for a and b!

So,

                                       [tex]21=a(b)^0[/tex]

and

                                        [tex]3=a(b)^1[/tex].

Solving the first equation we get,

                                         [tex]21=a(1)\\\Longrightarrow a=21[/tex].

We can plug the a value into the second equation to get b,

                                           [tex]3=21(b)^1\\\\3=21b\\\Longrightarrow \dfrac{1}{7}=b[/tex].

So our function is,

                                         [tex]y=21\left(\dfrac{1}{7}\right)^x[/tex].

Geometric Solution:

Knowing that all y-intercepts have an x-value of 0, we can identify that one of the points or solutions given in the problem is our y-intercept: (0, 21). Thus, a = 21.

From the two points given, we can see that as x gets bigger in the positive direction, the y-value decreases indicating that this is a decay function.

To be specific, we see that the y-value decreases from 21 to one-seventh of its value: 3. So, b = 1/7.

Plugging in our a and b values into the function we get,

                                            [tex]y=21\left(\dfrac{1}{7}\right)^x[/tex].

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.