pre-calc
One day, a controversial video is posted on the Internet that seemingly gives concrete evidence of life on other planets. Suppose that 50 people see the video the first day after it is posted and that this number doubles everyday after that.
a) write an expression to describe the number of people who have seen the video t days after it is posted.
b) one week later, a second video is posted that reveals the first as a hoax. Suppose that 20 people see this video the first day after it is posed and that this number triples every day after that. Write an expression to describe the number of people who have seen the 2nd video t days after it is posted.
c) set the two expressions from parts a and b to equal each other and then solve for t. What does this solution mean?
a) To describe the number of people who have seen the video t days after it is posted, we can use the following expression:
Number of people = 50 * 2^(t-1)
In this expression, t represents the number of days after the video is posted. The initial number of people who have seen the video is 50, and then it doubles each day afterward.
b) To describe the number of people who have seen the second video t days after it is posted, we can use the following expression:
Number of people = 20 * 3^(t-1)
In this expression, t represents the number of days after the second video is posted. The initial number of people who have seen the second video is 20, and then it triples each day afterward.
c) To set the two expressions equal to each other and solve for t, we can substitute the expressions from parts a and b:
50 * 2^(t-1) = 20 * 3^(t-1)
We can divide both sides of the equation by 10 to simplify it:
5 * 2^(t-1) = 2 * 3^(t-1)
We can further divide both sides by 2:
5 * 2^(t-2) = 3^(t-1)
Now, we have both sides of the equation in terms of powers of 2 and 3. To solve for t, we can equate the exponents:
t - 2 = t - 1
Simplifying further, we can subtract t from both sides:
-2 = -1
This equation does not have a solution. It means that there is no value of t that makes the number of people who have seen the first video equal to the number of people who have seen the second video at any given point in time.