Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Let's break down the steps to answer the question about the function representing the relationship between the number of days ([tex]$t$[/tex]) and the number of orders remaining.
Given:
- The store has 3000 orders initially.
- Each day, the store completes one-fourth of the remaining orders.
To find the function, let’s denote the number of orders remaining as [tex]$f(t)$[/tex] where [tex]$t$[/tex] is the number of days.
1. Initial Condition (Day 0):
At [tex]$t = 0$[/tex], the number of orders is 3000.
2. Day 1:
By the end of the first day, one-fourth of the initial orders are completed. So, [tex]\( \frac{3}{4} \)[/tex] of the orders remain.
Therefore, the number of orders remaining, [tex]$f(1)$[/tex], is:
[tex]\[ f(1) = 3000 \times \left( \frac{3}{4} \right) = 2250 \][/tex]
3. Day 2:
At [tex]$t = 2$[/tex], again one-fourth of the remaining orders from day 1 is completed. So, [tex]\( \frac{3}{4} \)[/tex] of the orders from day 1 remain.
[tex]\[ f(2) = 2250 \times \left( \frac{3}{4} \right) = 1687.5 \][/tex]
4. Day 3:
Similarly, at [tex]$t = 3$[/tex], one-fourth of the remaining orders from day 2 is completed. Thus, [tex]\( \frac{3}{4} \)[/tex] of the orders from day 2 remain.
[tex]\[ f(3) = 1687.5 \times \left( \frac{3}{4} \right) = 1265.625 \][/tex]
Following this pattern, for any day [tex]$t$[/tex], the function that describes the number of orders remaining can be written as an exponential decay function:
[tex]\[ f(t) = 3000 \times \left( \frac{3}{4} \right)^t \][/tex]
This matches with one of the provided options. The correct function is:
[tex]\[ f(t) = 3000 \cdot\left(\frac{3}{4}\right)^t \][/tex]
Thus, the correct answer for the given question is:
[tex]\[ f(t) = 3.000 \cdot\left(\frac{3}{4}\right)^t \][/tex]
Given:
- The store has 3000 orders initially.
- Each day, the store completes one-fourth of the remaining orders.
To find the function, let’s denote the number of orders remaining as [tex]$f(t)$[/tex] where [tex]$t$[/tex] is the number of days.
1. Initial Condition (Day 0):
At [tex]$t = 0$[/tex], the number of orders is 3000.
2. Day 1:
By the end of the first day, one-fourth of the initial orders are completed. So, [tex]\( \frac{3}{4} \)[/tex] of the orders remain.
Therefore, the number of orders remaining, [tex]$f(1)$[/tex], is:
[tex]\[ f(1) = 3000 \times \left( \frac{3}{4} \right) = 2250 \][/tex]
3. Day 2:
At [tex]$t = 2$[/tex], again one-fourth of the remaining orders from day 1 is completed. So, [tex]\( \frac{3}{4} \)[/tex] of the orders from day 1 remain.
[tex]\[ f(2) = 2250 \times \left( \frac{3}{4} \right) = 1687.5 \][/tex]
4. Day 3:
Similarly, at [tex]$t = 3$[/tex], one-fourth of the remaining orders from day 2 is completed. Thus, [tex]\( \frac{3}{4} \)[/tex] of the orders from day 2 remain.
[tex]\[ f(3) = 1687.5 \times \left( \frac{3}{4} \right) = 1265.625 \][/tex]
Following this pattern, for any day [tex]$t$[/tex], the function that describes the number of orders remaining can be written as an exponential decay function:
[tex]\[ f(t) = 3000 \times \left( \frac{3}{4} \right)^t \][/tex]
This matches with one of the provided options. The correct function is:
[tex]\[ f(t) = 3000 \cdot\left(\frac{3}{4}\right)^t \][/tex]
Thus, the correct answer for the given question is:
[tex]\[ f(t) = 3.000 \cdot\left(\frac{3}{4}\right)^t \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.