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Natalija [7]
2 years ago
6

Mattie Evans drove 200 miles in the same amount of time that it took a turbo propeller plane to travel 800 miles. The speed of t

he plane was 150 mph faster than the speed of the car. Find the speed of the plane.
Mathematics
1 answer:
Andru [333]2 years ago
8 0

Answer:

<em>200mph</em>

Step-by-step explanation:

Speed is expressed using the expression

Speed = Distance/Time

For Mattie

Distance = 200miles

Speed = x

Time taken by mattie = Distance/speed

Time taken by mattie = 200/x ... 1

For the propeller plane:

Distance = 800miles

Speed = x+150 (The speed of the plane was 150 mph faster than the speed of the car)

time taken by the plane = 800/x+150

Since Mattie took the same amount of time that it took a turbo propeller plane to travel, then we will equate both expressions as shown:

200/x = 800/150+x

Cross multiply

800x = 200(150+x)

800x = 30,000 + 200x

800x-200x = 30,000

600x = 30,000

x = 30,000/600

x = 50

Get the speed of the plane

Since the speed of the plane is 150+x

Speed of the plane = 150+50

<em>Speed of the plane = 200mph</em>

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5
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<h2>                      Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

f\left(x\right)\:=\:3\left(5\right)^x

The growth factor between x=1 and x=3 is given by:

\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]

\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375

\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15

So,

= 375\div \:15

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Similarly, growth factor between x=5 and x=7 is given by:

\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]

= \frac{3\cdot \:5^7}{3\cdot \:5^5}

\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1

= \frac{5^7}{5^5}

\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}

\frac{5^7}{5^5}=5^{7-5}

= 5^{7-5}

= 5^2

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Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2>                         Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as y=A\cdot \left(b\right)^t is an exponential function.

The graph for y=A\cdot \left(b\right)^t is also shown in attached figure.

Step-by-step explanation:

  • If a city that currently has a population of 1000 triples in size every 8 years.
  • what will the population be in 24 years?
  • Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

y=A\cdot \left(b\right)^t

where

A = Initial population amount

b = growth rate

t = time

Substituting the values in the function

y=A\cdot \left(b\right)^t

y=1000\cdot \:\:3^{\frac{1}{8}t}

So, the population be in 24 years

y=1000\cdot \:\:3^{\frac{1}{8}24}

As

3^{\frac{1}{8}\cdot \:24}=3^3

So

\:y=3^3\cdot 1000

y=1000\cdot \:\:27

y=27000

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as y=A\cdot \left(b\right)^t is an exponential function.

<h2 /><h2>                       Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function f(x)=2x when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

  • Given a function f(x), and a constant c > 0, the function g(x) = f(x - a) represents a horizontal shift c units to the right from f(x). The function h(x) = f(x + a) represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

#learnwithBrainly

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