The following table gives the distance f(t) fallen by a smoke...

Question

The following table gives the distance f(t) fallen by a smoke jumper seconds after she opens her chute.

a. Use the forward difference quotient with ℎ = 0.5 to estimate the velocity of the smoke jumper at t=2 seconds.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A scientist is studying the growth of a bacterial culture. The population of the bacteria PFT in thousands at time T in hours is given in the following table. T in units of hours is 00.2, 0.4, 0.6, 0.8, 1.0. And P of T in units of thousands is 5.00, 5.91, 6.96, 8.16, 9.53, 11.08. Use the forward difference quotient with H equals 0.2 to estimate the growth rate of the bacterial population at T equals 0.6 hours. Or 0.6 hours hour. So, because it's not a full hour yet. So, with that in mind, so our end goal, the final answer that we're ultimately trying to solve for is we're trying to recall and use. The forward difference quotient equation with the value of H being 0.2 to help us estimate the growth rate of the bacterial population at T equals 0.6 hour. So once again, we're trying to estimate the growth rate of the bacterial population at a specific value of T. So with that in mind, let's read off our multiple choice answers to see what our final answer might be, noting that they're all going to be in the same units of 1000 per hour. So A is 4.55, B is 7.75. And C is 6.00, and D is 6.85. OK. So first off, we need to recall and use the formula for the forward difference quotient, which states that P of T will be approximately equal to P T plus H. Minus PFT. All divided by H. Fantastic. So that's our expression for the formula for the forward difference quotient. Noting that capital P denotes our population. And T denotes our time. So now, when we plug in our value for tea, we could write. Our expression as P 0.6 is approximately equal to P. Of 0.6 plus 0.2, because that's our value for H is 0.2. Minus P of 0.6. Awesome, and don't forget your parenthesis, and let's move this over a little bit because we're. Running out of space here, so we need to take Her expression and shifted over just a hair here. Awesome. So now, Once again, let's quickly recap here. So P 0.6 is approximately equal to P of 0.6 plus 0.2 minus P of 0.6, and don't forget that this will be all divided by our value for H, which once again is 0.2. So that will mean that this whole expression is approximately equal to P of 0.8 minus P of 0.6. All divided by 0.2. So according to our table, we should recall. And note that P of 0.6 is going to be equal to 8.16 and P of 0.8. It's going to be equal to 9. 53 As specified in our table. So therefore, as a result, P 0.6 will be approximately equal to 9.53 minus 8.16 divided by 0.2. So that will mean that P 0.6 will be approximately equal to 6.85 when we round to two decimal places, and it's units of measurement will be 1000. hour. And that's it. That is our final answer. Hooray, we did it. And this corresponds with multiple choice answer letter D, which once again is 6.85,000 per hour. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

The following table gives the distance f(t) fallen by a smoke jumper seconds after she opens her chute. <IMAGE>
a. Use the forward difference quotient with ℎ = 0.5 to estimate the velocity of the smoke jumper at t=2 seconds.

Watch next

The following table gives the ​distance f(t) fallen by a smoke jumper seconds after she opens her chute​. <IMAGE>a. Use the forward difference quotient with ℎ = 0.5 to estimate the velocity of the smoke jumper at t=2 seconds.

Watch next

The following table gives the distance f(t) fallen by a smoke jumper seconds after she opens her chute. <IMAGE>
a. Use the forward difference quotient with ℎ = 0.5 to estimate the velocity of the smoke jumper at t=2 seconds.