Question
Jamie and Linda are having a contest to see whose photo will get more "likes" on social media.
Jamie's photo got 75 likes by the end of the first day and is getting 36 more likes each day.
Linda's likes can be modeled by the function f(x)=18(2)x.
Which statements are true? Select all that apply.
Hint: Use a table or graph to compare the number of likes that Jamie and Linda get. Remember that the value of the function at x=1 represents number of likes at the end of the first day.
1. Jamie's photo gets more likes within the first three days than Linda's photo.Jamie's photo gets more likes within the first three days than Linda's photo. , ,
2. It takes Linda's photo 5 days to have more likes than Jamie's photo.It takes Linda's photo 5 days to have more likes than Jamie's photo. , ,
3. Linda's photo gets more likes within the first three days.Linda's photo gets more likes within the first three days. , ,
4. Jamie's photo will always have more likes than Linda's.Jamie's photo will always have more likes than Linda's. , ,
5. On day 4, Linda's photo will have over 100 more likes than Jamie's photo.
To determine which statements are true, let's analyze the given information step by step.
Jamie's photo gets 75 likes by the end of the first day and is getting 36 more likes each day. We can create a table to track the number of Jamie's likes:
| Day | Number of Likes |
| ------ | -------------- |
| 1 | 75 |
| 2 | 75+36=111 |
| 3 | 75+36+36=147 |
| 4 | 75+36+36+36=183 |
Linda's likes can be modeled by the function f(x) = 18(2)^x. Using this function, we can calculate the number of Linda's likes for each day:
| Day | Number of Likes |
| ------ | -------------- |
| 1 | 18(2)^1=36 |
| 2 | 18(2)^2=72 |
| 3 | 18(2)^3=144 |
| 4 | 18(2)^4=288 |
Now let's analyze the statements:
1. Jamie's photo gets more likes within the first three days than Linda's photo.
=> Looking at the table, this statement is false. On day 3, Jamie has 147 likes while Linda has 144 likes.
2. It takes Linda's photo 5 days to have more likes than Jamie's photo.
=> Since Linda's likes are growing at an exponential rate, at some point, she will surpass Jamie's likes. However, based on the data provided, it will not happen on day 5. Therefore, this statement is false.
3. Linda's photo gets more likes within the first three days.
=> Looking at the table, this statement is false. Jamie's photo has more likes than Linda's photo within the first three days.
4. Jamie's photo will always have more likes than Linda's.
=> Based on the given information, Jamie's photo is receiving an additional 36 likes each day, while Linda's photo is growing exponentially at a rate that starts with 18 and doubles with each day. Since Jamie's likes are increasing at a constant rate, while Linda's are growing exponentially, it is not possible to say that Jamie's photo will always have more likes than Linda's. This statement is false.
5. On day 4, Linda's photo will have over 100 more likes than Jamie's photo.
=> Looking at the table, on day 4, Linda has 288 likes and Jamie has 183 likes. Therefore, Linda's photo will indeed have over 100 more likes than Jamie's photo on day 4. This statement is true.
In conclusion, the true statements are:
- On day 4, Linda's photo will have over 100 more likes than Jamie's photo.
To determine which statements are true, we can construct a table or graph to compare the number of likes that Jamie and Linda's photos receive over time.
Let's start by calculating the number of likes Jamie's photo receives each day:
Day 1: 75 likes
Day 2: 75 + 36 = 111 likes
Day 3: 111 + 36 = 147 likes
Now let's calculate the number of likes Linda's photo receives each day using the function f(x) = 18(2)^x:
Day 1: f(1) = 18(2)^1 = 18(2) = 36 likes
Day 2: f(2) = 18(2)^2 = 18(4) = 72 likes
Day 3: f(3) = 18(2)^3 = 18(8) = 144 likes
Now we can examine the statements one by one:
1. Jamie's photo gets more likes within the first three days than Linda's photo.
Checking the table/graph, we can see that Jamie's photo has more likes than Linda's photo in the first three days. This statement is true.
2. It takes Linda's photo 5 days to have more likes than Jamie's photo.
Based on the table/graph, we can see that Linda's photo doesn't have more likes than Jamie's photo within the first 5 days. This statement is false.
3. Linda's photo gets more likes within the first three days.
By comparing the number of likes in the table/graph, we can see that Jamie's photo has more likes than Linda's photo in the first three days. This statement is false.
4. Jamie's photo will always have more likes than Linda's.
Based on the information given, there is no evidence to support that Jamie's photo will always have more likes than Linda's photo. This statement is false.
5. On day 4, Linda's photo will have over 100 more likes than Jamie's photo.
Checking the table/graph, we can see that on day 4, Linda's photo has 144 likes while Jamie's photo has 183 likes. Linda's photo does not have over 100 more likes than Jamie's photo on day 4. This statement is false.
To summarize, the true statements are:
1. Jamie's photo gets more likes within the first three days than Linda's photo.