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NeX [460]
3 years ago
8

The value of a $3000 computer decreases about 30% each year. write a function for the computers value V(t)

Mathematics
2 answers:
Viefleur [7K]3 years ago
8 0

Answer:

A = $3000(0.70)^t

Step-by-step explanation:

100% - 30% = 70%.  Thus, the common ratio in this exponential function is 0.70.

Use a formula with the form of the compound amount formula:

A = P(1 + r)^t, where r is the common ratio as a decimal fraction and t is the number of years.

Here, A = $3000(1 - 0.30)^t, or    A = $3000(0.70)^t

den301095 [7]3 years ago
7 0

Answer:

Function for given situation is : V(t)=3000(0.70)^t

Value of computer after 4 years = $720.3.

Step-by-step explanation:

Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then we need to find about how much will the computer be worth in 4 years.

It clearly says that value decreases so that means function represents decay.

For decay we use formula:

A=P(1-r)^t

where P=initial value = $3000,

r= rate of decrease =30% = 0.30

t= number of years

A=V(t) = future value

so the required function is V(t)=3000(1-0.30)^t

or V(t)=3000(0.70)^t

Now plug t=4 years to get the value of computer after 4 years.

V(4)=3000(0.70)^4

V(4)=720.3

Hence final answer is $720.3.

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The box which measures 70cm X 36cm X 12cm is to be covered by a canvas. How many meters of canvas of width 80cm would be require
grigory [225]

Answer:

142.2 meters.  

Step-by-step explanation:

We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.      

Let us find total surface area of box using surface area formula of cuboid.

\text{Total surface area of cuboid}=2(lb+bh+hl), where,

l = Length of cuboid,

b = Breadth of cuboid,

w = Width of cuboid.

\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)

\text{Total surface area of box}=2(2520+432+840)

\text{Total surface area of box}=2(3792)

\text{Total surface area of box}=7584

Therefore, the total surface area of box will be 7584 square cm.  

To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.

\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}

80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2

\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}

\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}

\text{ Length of canvass}=14220\text{ cm}

Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.

\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}

\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}

\text{ Length of canvass}=\frac{14220\text{ cm}}{100}\times\frac{m}{cm}

\text{ Length of canvass}=142.20\text{ m}

Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.

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3 years ago
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musickatia [10]
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