1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SIZIF [17.4K]
2 years ago
5

The graph of an exponential function passes through (1, 10) and (4, 80). Find the function that describes the graph.

Mathematics
2 answers:
Otrada [13]2 years ago
7 0

Answer:

y=5 \cdot 2^x

Step-by-step explanation:

An exponential function is written in the form:

  • y=ab^x

We can use the given points that the exponential function passes through to solve for a and b.

Create a system of equations by substituting <u>(1, 10)</u> and <u>(4, 80)</u> into the exponential form of a function.

  • \text{I}:\ 10=ab^1
  • \text{II}: \ 8 0=ab^4

Divide Equation I by Equation II in order to cancel out variable a.

  • \displaystyle \frac{80=ab^4}{10=ab}
  • 8=b^3
  • b=2

Now we can solve for a by substituting b back into either equation from the system of equations.

  • 10=ab
  • 10=a(2)
  • a=5

Substitute 5 for a and 2 for b into the form of an exponential function to find the exponential function that passes through (1, 10) and (4, 80).

  • y=5 \cdot 2^x

y = 5 · 2ˣ is the exponential function that describes the graph.

svetlana [45]2 years ago
4 0

Answer:

  • y = 5*2ˣ

Step-by-step explanation:

<u>Exponential function:</u>

  • y = abˣ

<u>Ordered pairs given:</u>

  • (1, 10) and (4, 80)

<u>Substitute x and y values to get below system:</u>

  • 10 = ab
  • 80 = ab⁴

<u>Divide the second equation by the first one and solve for b:</u>

  • 80/10 = b³
  • b³ = 8
  • b = ∛8
  • b = 2

<u>Use the first equation and find the value of a:</u>

  • 10 = a*2
  • a = 5

<u>The function is:</u>

  • y = 5*2ˣ
You might be interested in
A mole starts out in its burrow 5.1 feet below the surface of the ground. It digs straight up at a rate of 0.4 feet per minute.
bearhunter [10]

Answer:

12.75

Step-by-step explanation:

you divide

I like burgers but not meat I like fish burgers what about you

7 0
2 years ago
Read 2 more answers
HURRY FAST REPLIESSS
telo118 [61]

Answer:

14.8

Step-by-step explanation:

13^2 + 7^2 = 218

sqrt(218) = 14.76

8 0
3 years ago
The most popular items at a bakery are its raspberry scones and its lemon poppy
Leno4ka [110]

The system r+l = 46 and 15r + 9l = 396 can be used to determine the number of raspberries boxes and lemon seed boxes sold.

Step-by-step explanation:

Given,

Cost per box of raspberry = $15

Cost per box of lemon seeds = $9

Total boxes sold = 46

Total revenue generated = $396

Let,

r represent the number of raspberries sold

l represent the number of lemon seeds sold

According to given statement;

r+l = 46    Eqn 1

15r + 9l = 396    Eqn 2

The system r+l = 46 and 15r + 9l = 396 can be used to determine the number of raspberries boxes and lemon seed boxes sold.

7 0
3 years ago
20 points!
Sveta_85 [38]

Translations, rotations, and reflections are all rigid transformations.

8 0
3 years ago
Read 2 more answers
Find the slope of the line using the table. (keep as a fraction)
attashe74 [19]
The slope is -2/3 or -2 over 3
8 0
3 years ago
Other questions:
  • At a shelter 15% of the dogs are puppies. There are 60 dogs at the shelter. How many are puppies?
    5·2 answers
  • At a baseball game, the probability that a fan brings a glove is 0.08. The probability that a fan is left-handed is 0.12. What i
    6·2 answers
  • Factor the polynomial completely using the x method. x^2 + 11x + 24
    15·1 answer
  • Trick question what is 1+(6+8)×3? Did you get it correct?
    10·2 answers
  • Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. R
    6·1 answer
  • Which is the correct statement <br> 3/32&lt; 5/32, 3/32&gt;5/32, 3/32=5/32
    13·1 answer
  • Find the second term of the arithmetic series described by a = -10, an = 26 and Sn = 200. 1. 1.5 2. -8.5 3. 16 4. 25
    10·1 answer
  • Select the graph of the quadratic function g(x) = 2x2. Identify the domain and range
    8·1 answer
  • This morning, Josh's car had 19.22 gallons of fuel. Now, 5.3 gallons are left. How much fuel did Josh use?​
    7·2 answers
  • Solve for x. x = [?] = 5x - 73x + 27 Enter​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!