Question

The price of a computer component is decreasing at a rate of 11% per year. State whether

this decrease is linear or exponential. If the component costs $120 today, what will it cost
in three years?
Is the decline in price linear or exponential?
linear
O exponential

Answer 1

The price decrease of the computer component is exponential. By using the exponential decay formula, the cost of the component that is $120 today will be approximately $84.96 in three years.

Step-by-step explanation:

The decline in the price of a computer component that decreases at a rate of 11% per year is an exponential decline. This is because the price reduction each year is based on the current price of the component, not a fixed amount. To calculate the cost three years from now, we can use the formula for exponential decay:

New Value = Original Value × (1 - Rate of Decrease)^Number of Periods

If today's price is $120, the cost after three years would be:

New Price = $120 × (1 - 0.11)^3

New Price = $120 × (0.89)^3

New Price = $120 × 0.708

New Price = $84.96 (rounded to two decimal places)

Therefore, if the component costs $120 today, it will cost approximately $84.96 in three years.

Answer 2

• The decrease is Linear.
• The component will cost $84.59 in 3 years
• The decline in price is Exponential.

Step-by-step explanation:

Question 1:

In this question, it's asking you if the decreasing rate is linear or exponential.

The decreasing rate would be linear, due to the fact that it is decreasing at a constant rate of 11%. The decreasing rate doesn't change, which makes this linear.

Question 2:

In this question, it's asking you what would the component's cost be in 3 years if it started off at $120.

To find this, we're going to need multiply the price by -.11, and then subtract to get the price. We would repeat this until we reach 3 years.

Work:

`120*-0.11=-13.2\\\\120-13.2=106.8\ \text{(Year 1)}\\\\106.8*-0.11= -11.748\\\\106.8-11.748=95.05\ \text{(Year 2)}\\\\95.05*-0.11=-10.4555\\\\95.05-10.4555=84.59\ \text{(Year 3)}\\\\\text{In year 3, the cost of the component would be \$84.59}`

Question 3:

In this question, it asks if the decline in price is linear or exponential.

The decline in price would be exponential, due to the fact that the decrease in price is not always the same, since it changes every year. The price doesn't decrease at the same price each year. As you see from question 2, the change in price is not the same each year.

I hope this helps you out.

Good luck on your academics.

Have a fantastic day!