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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
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I need this answered Fast if possible. A car is traveling on a small highway and is either going 55 miles per hour or 35 miles
Alex787 [66]

a. It spends about 2.045 hours going 55 miles per hour

b. It spends 1 hour going 35 miles per hour

c. The trip would take about 3.64 hours

Step-by-step explanation:

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles  per hour, depending on the speed limits, until it reaches its destination 200 miles  away

  • x represents the amount of time in hours that the car is going 55 miles per  hour
  • y represents the amount of time in hours that the car is going 35 miles per hour
  • The equation  that describing the relationship is 55x + 35y = 200

We need to find:

a. How long does it  spend going 55 miles per hour, if the car spends 2.5 hours going 35 miles per hour on the trip

∵ 55x + 35y = 200

∵ The car spends 2.5 hours going 35 miles per hour on the trip

∵ y represents the amount of time that the car going 35 mi./h

∴ y = 2.5

- Substitute the value of y in the equation to find the value of x

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Subtract 87.5 from both sides

∴ 55x = 112.5

- Divide both sides by 55

∴ x = 2.045 hours

It spends about 2.045 hours going 55 miles per hour

b.how long does it  spend going 35 miles per hour, if the car spends 3 hours going 55 miles per hour on the trip

∵ 55x + 35y = 200

∵ The car spends 3 hours going 55 miles per hour on the trip

∵ x represents the amount of time that the car going 55 mi./h

∴ x = 3

- Substitute the value of y in the equation to find the value of x

∴ 55(3) + 35y = 200

∴ 165 + 35y = 200

- Subtract 165 from both sides

∴ 35y = 35

- Divide both sides by 35

∴ y = 1 hour

It spends 1 hour going 35 miles per hour

c. How long would the trip take, if the car spends no time going 35 miles per hour

∵ 55x + 35y = 200

∵ The car spends no time going 35 miles per hour

∴ y = 0

- Substitute the value of y in the equation to find the value of x

∴ 55x + 35(0) = 200

∴ 55x  = 200

- Divide both sides by 55

∴ x = 3.63 hours

The trip would take about 3.64 hours

Learn more:

You can learn more about the equations in brainly.com/question/4097107

#LearnwithBrainly

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