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• - [Instructor] We are told a phone sells for \$600

• and loses 25% of its value per year.

• Write a function that gives the phone's value, V of t,

• so value as a function of time, t years after it is sold.

• So pause this video, and have a go at that

• before we work through it together.

• All right, so let's just think about it a little bit.

• And I could even set up a table

• to think about what is going on.

• So this is t, and this is the value of our phone

• as a function of t.

• So it sells for \$600.

• At time t equals zero, what is V of zero?

• Well it's going to be equal to \$600.

• That's what it sells for at time t equals zero.

• Now at t equals one, what's going to happen?

• Well it says that the phone loses 25%

• of its value per year.

• Another way to rewrite that it loses 25% of its value

• per year is that it retains, it retains,

• 100% minus 25% of its value per year,

• or it retains 75%

• of its value per year, per year.

• So how much is it going to be worth after one year?

• Well it's going to be worth \$600,

• \$600 times 75%.

• Now what about year two?

• Well it's going to be worth what it was in year one

• times 75% again.

• So it's going to be \$600 times 75% times 75%.

• And so you could write that as times 75% squared.

• And I think you see a pattern.

• In general, if we have gone, let's just call it t years,

• well then the value of our phone,

• if we're saying it in dollars, is just going to be \$600

• times, and I could write it as a decimal,

• 0.75, instead of 75%, to the t power.

• So V of t is going to be equal to 600

• times 0.75 to the t power, and we're done.

• Let's do another example.

• So here, we are told that a biologist has a sample

• of 6,000 cells.

• The biologist introduces a virus that kills 1/3

• of the cells every week.

• Write a function that gives the number of cells remaining,

• which would be C of t, the cells as a function of time,

• in the sample t weeks after the virus is introduced.

• So again, pause this video

• and see if you can figure that out.

• All right, so I'll set up another table again.

• So this is time, it's in weeks,

• and this is the number of cells, C.

• We could say it's a function of time.

• So time t equals zero, when zero weeks have gone by,

• we have 6,000 cells.

• That's pretty clear.

• Now after one week, how many cells do we have?

• What's C of one?

• Well it says that the virus kills 1/3

• of the cells every week, which is another way of saying

• that 2/3 of the cells are able to live

• for the next week.

• And so after one week, we're going to have 6,000 times 2/3.

• And then after two weeks, or another week goes by,

• we're gonna have 2/3 of the number that we had

• after one week.

• So we're gonna have 6,000 times 2/3 times 2/3,

• or we could just write that as 2/3 squared.

• So once again, you are likely seeing the pattern here.

• We are going to, at time t equals zero, we have 6,000,

• and then we're going to multiply by 2/3

• however many weeks have gone by.

• So the cells as a function of the weeks of t,

• which is in weeks, is going to be our original amount,

• and then however many weeks have gone by,

• we're going to multiply by 2/3 that many times,

• so times 2/3 to the t power.

• And we're done.

- [Instructor] We are told a phone sells for \$600

A2 初級

# 指數衰落單詞問題 (Exponential decay word problems)

• 1 0
林宜悉 發佈於 2021 年 01 月 14 日