The Price Of A Computer Component Is Decreasing At A Rate Of 11 Pe 1. The price of a computer component is decreasing at a rate of 11% per year. Determine whether this decrease is linear or exponential. Given that the component costs $80 today, calculate its cost after three years. Is the decline in price linear or exponential? What will the component cost in three years? 2. A leprechaun places a magic penny under a girl's pillow. The next night, there are 2 magic pennies under her pillow. Each night, the number of magic pennies doubles. How much money will the girl have after 16 nights? 3. Decide whether the following statement makes sense or is clearly false: “I graphed two linear functions, and the one with the greater rate of change had the greater slope.” Explain your reasoning. 4. The following situation can be modeled by a linear function. Write an equation for the linear function, identify the independent and dependent variables, and assess whether a linear model is appropriate. A copy center rents computer time for a $7 setup fee plus $3.50 for every ten minutes. How much time can be rented for $22? A. The independent variable is rental cost (r), in dollars, and the dependent variable is time (t), in minutes. The linear function modeling this is t= (provide simplified form). How many minutes can be rented for $22? B. The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function is r= (provide simplified form). Is a linear model reasonable for this situation? 5. Between 2005 and 2009, the average rate of inflation was about 4.5% per year. If a grocery cart cost $170 in 2005, what was its approximate cost in 2009?
Paper For Above instruction Understanding the nature of percentage decreases and exponential growth or decay is essential in numerous real-world applications, from economics to environmental science. The first problem involves a computer component priced at $80 with an annual decrease of 11%. This scenario represents exponential decay, not linear decrease, because the percentage decrease is applied to the current price each year, leading to a compound effect. The exponential decay formula is P(t) = P_0 * (1 - r)^t, where P_0 is the initial price, r is the rate of decrease, and t is time in years. For this case, P(3) = 80 * (1 - 0.11)^3 ≈ 80 * 0.89^3 ≈ 80 * 0.7049 ≈ $56.39. This calculation indicates the price after three years will be approximately