High School

Exponential Functions 1-1 Practice

Write each geometric sequence as an exponential function. Graph the function for all integers, n, such

that 1 ≤ n ≤ 10.

1.)9n=5 2n-1

2.) 9n=-3-3-1

fn=

3000

fn=

-12000-

2400

1800

1200

600

2

-24000

-36000

-60000

+

4

6

8

10

y

9

8

Exponential Functions 1 1 Practice Write each geometric sequence as an exponential function Graph the function for all integers n such that 1 n 10

Answer :

To write each geometric sequence as an exponential function, we need to identify the pattern of change between the terms and express it in the form of [tex]f(n) = a \cdot r^{n-1}[/tex], where [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio.

Let's evaluate each case:

  1. Sequence: [tex]9, 5, 2n-1[/tex]

    First, let's determine the first term [tex]a[/tex]. In this case, the first term is given as 9.

    Next, we need to identify the common ratio [tex]r[/tex]. Since the sequence only lists initial terms as [tex]9, 5[/tex], it seems we lack complete information about [tex]2n - 1[/tex]. To write a function, more information is needed.

  2. Sequence: [tex]-3, -3, -1[/tex]

    Here, the terms seem to be incorrect or incomplete, so let’s construct based on what typical geometric sequences offer. With an appropriate sequence:

    • Let's consider a potential pattern cause from [tex]-3[/tex]. Common differences are not apparent though. Unable to identify exact ubiquitous sequence here with numbers provided.

    Given the defined structure, expressing the problem with regards to graphing could offer insight:

  3. Assuming proper sequence continuation, [tex]f(n)[/tex] relies on further given traits typically involving [tex]a[/tex] and correctly solved common [tex]r[/tex] which is beyond provided values here.

In general, sequences need further digits or patterns effectively beyond provided examples. Review textual items for any overlooked traits showing more sequences. Each sequence need appropriate numbers to confirm the sequence; elements in this item return confusing initial assumptions clarified by seeing patterns.

To graph functional values [tex]1 \leq n \leq 10[/tex], formal calculations after deriving values must provide function output or clarification from—[tex]a[/tex]—missing or suspect. The graph of such expressions spans multiple layers when details integrate cleanly.

Without required data receiving appropriate answers can be challenged; informations like [tex]-12000[/tex] typically point though full math steps remain void when presented incomplete figures. Acquiring accurate parts leads easily ready depiction.

Final answer:

The exponential functions are f(n) = 5·2^(n-1) and f(n) = -3·(-3)^(n-1) for 1 ≤ n ≤ 10. Calculate and plot their values for each integer n to complete the graphs.

Explanation:

Writing Geometric Sequences as Exponential Functions


1. For 9n = 5·2^(n-1):


This is already in the form of an exponential function. The first term (when n=1) is 5·2^(1-1) = 5·1 = 5. The common ratio is 2. So, the exponential function is:


f(n) = 5·2^(n-1)


2. For 9n = -3·(-3)^(n-1):


This is also in the form of an exponential function. The first term (when n=1) is -3·(-3)^(1-1) = -3·1 = -3. The common ratio is -3. So, the exponential function is:


f(n) = -3·(-3)^(n-1)


Graphing the Functions



  1. For f(n) = 5·2^(n-1), calculate values for n = 1 to 10:

    • n=1: 5·2^0 = 5

    • n=2: 5·2^1 = 10

    • n=3: 5·2^2 = 20

    • n=4: 5·2^3 = 40

    • n=5: 5·2^4 = 80

    • n=6: 5·2^5 = 160

    • n=7: 5·2^6 = 320

    • n=8: 5·2^7 = 640

    • n=9: 5·2^8 = 1280

    • n=10: 5·2^9 = 2560



  2. For f(n) = -3·(-3)^(n-1), calculate values for n = 1 to 10:

    • n=1: -3·(-3)^0 = -3

    • n=2: -3·(-3)^1 = 9

    • n=3: -3·(-3)^2 = -27

    • n=4: -3·(-3)^3 = 81

    • n=5: -3·(-3)^4 = -243

    • n=6: -3·(-3)^5 = 729

    • n=7: -3·(-3)^6 = -2187

    • n=8: -3·(-3)^7 = 6561

    • n=9: -3·(-3)^8 = -19683

    • n=10: -3·(-3)^9 = 59049




Plot these points on the provided graphs, with n on the x-axis and f(n) on the y-axis. The first function will show exponential growth, while the second will alternate between positive and negative values, growing rapidly in magnitude.

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