Can a pair of numbers have more than one common factor?
1 answer:
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Answer:
See below.
Step-by-step explanation:
1)
For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:
The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.
2)
Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:
The 10 represents the initial amount while the 2 represents the rate.
3)
I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.
4)
To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:
For Amber:
Day 3:
Day 10:
For Ben:
Day 3:
Day 10:
And for Carter:
Day 3:
Day 10:
5)
Amber's new graph of:
will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.
6)
On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.
7)
If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.
The function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.
<h3>What is an exponential function?</h3>It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent
where a is a constant and a>1
We have; an exponential function that passes through the point (2, 80).
f(x) = 4(x)⁵
Plug (2, 80) in the abovew function:
f(2) = 4(2)⁵ = 128 (false)
f(x) = 5(x)⁴
Plug (2, 80) in the abovew function:
f(2) = 5(2)⁴ = 80 (true)
f(x) = 4(5)ˣ
f(2) = 4(5)² = 100 (false)
f(x) = 5(4)ˣ
f(2) = 5(4)² = 80 (true)
Thus, the function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.
Learn more about the exponential function here:
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