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?
Ok can you just check my answers for parts a and b, except for part c i don't know what this means.
a) A(t)=50(2)^t
b) A(t)=20(3)^t
c) I set them equal to each other and the variable disappeared on me..ie cancelled out What does this mean?
right on a,b.
50 2^t = 20 3^t
take the log of each side
log50 + t*log2 = log 20 + t log3
solve for t
log to any base, your calculator is your friend on this.
Ok but I have
log50-log20=tlog3-tlog2
Now what?
log50-log20=tlog(3/2)
Your answers for parts a and b are correct:
a) A(t) = 50(2)^t
b) A(t) = 20(3)^t
In part c, setting the two expressions equal to each other and solving for t means finding the value of t where the number of people who have seen the first video is equal to the number of people who have seen the second video.
Let's set up the equation:
50(2)^t = 20(3)^t
To solve for t, we need to isolate the variable on one side of the equation. Let's divide both sides by 20:
(50/20)(2)^t = (3)^t
Simplifying further:
(5/2)(2)^t = (3)^t
Next, let's divide both sides by (2)^t:
(5/2) = (3/2)^t
Now, to solve for t, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):
ln(5/2) = ln((3/2)^t)
Using the logarithmic property of exponents, we can bring the exponent down:
ln(5/2) = t * ln(3/2)
Finally, we solve for t by dividing both sides by ln(3/2):
t = ln(5/2) / ln(3/2)
The solution for t is the value you get when you calculate this expression.
In this context, finding the value of t means determining the number of days it will take for the number of people who have seen the first video to be equal to the number of people who have seen the second video.