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zubka84 [21]
3 years ago
11

The price of a computer component is decreasing at a rate of 15​% per year. State whether this decrease is linear or exponential

. If the component costs ​$60 ​today, what will it cost in three​ years? Is the decline in price linear or​ exponential?
Mathematics
1 answer:
Margaret [11]3 years ago
6 0

Answer:

Since the price is given by an exponential function, the decline in price is exponential.

The component will cost $36.8475 in three years.

Step-by-step explanation:

The equation for the price of a component has the following format:

P(t) = P(0)(1-r)^{t}

In which P(t) is the price after t years, P(0) is the initial price, and r is the rate that the price decreases.

Since the price is given by an exponential function, the decline in price is exponential.

The price of a computer component is decreasing at a rate of 15​% per year.

This means that r = 0.15

Component costs ​$60 ​today

So P(0) = 60. Then

P(t) = P(0)(1-r)^{t}

P(t) = 60(1-0.15)^{t}

P(t) = 60(0.85)^{t}

What will it cost in three​ years?

This is P(3).

P(t) = 60(0.85)^{t}

P(3) = 60(0.85)^{3} = 36.8475

The component will cost $36.8475 in three years.

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n+6 is less than or equal to 3

Step-by-step explanation:

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The height H of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 9
mariarad [96]

Answer:

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

Step-by-step explanation:

Statement is incorrect. Correct form is presented below:

<em>The height </em>h(t)<em> of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 90 feet per second is given by equation </em>h(t) = 3 +90\cdot t -16\cdot t^{2}<em>, where </em>t<em> is time in seconds. After how many seconds will the ball be 84 feet above the ground. </em>

We equalize the kinematic formula to 84 feet and solve the resulting second-order polynomial by Quadratic Formula to determine the instants associated with such height:

3+90\cdot t -16\cdot t^{2} = 84

16\cdot t^{2}-90\cdot t +81 = 0 (1)

By Quadratic Formula:

t_{1,2} = \frac{90\pm \sqrt{(-90)^{2}-4\cdot (16)\cdot (81)}}{2\cdot (16)}

t_{1} = 4.5\,s, t_{2} = 1.125\,s

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

3 0
2 years ago
Answer all the four q
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2 years ago
1.) Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation y = 5000 * (
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Answer:

a. The initial amount of money that was left in this savings account was of 5000.

b. Decrease of 2% each year.

Step-by-step explanation:

Exponential function:

An exponential function, with an initial value of A(0), and a decay rate of r, as a decimal, is given by:

A(t) = A(0)(1-r)^t

In this question, we have:

y = 5000*(0.98)^x

a. What was the initial amount of money that was left in this savings account?

This is y(0) = 5000

The initial amount of money that was left in this savings account was of 5000.

b. What is the percent of change each year in this savings account?

First as a decimal.

1 - r = 0.98

r = 1 - 0.98

r = 0.02

So a decrease of 2% each year.

7 0
2 years ago
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