A useful quantity for our purposes is the reproductive distance rate F of a geothermal vent....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A useful quantity for our purposes is the reproductive distance rate F of a geothermal vent. This measures how much the extremophiles reproduce per metre from the centre of the geothermal vent and has units of 104 bacteria per metre times seconds. For a generic vent, the distance rate F has been measured to give the following table. 1 1.5 2 2.5 3 3.5 4 0.2 -0.3 -0.8 -1.2 distance from vent (m) 0 0.5 F (10 bacteria/ms) 0 0.5 0.78 1 1.2 (a) (2 points) Write down (but do not evaluate!) an integral expression for the rate R at which extremophiles reproduce a given distance d away from the centre of the geothermal vent provided you know the rate of reproduction is 0 at the centre of the geothermal vent. (Hint: R has units 104 bacteria/s) (Hint: if I was constant, then R = Fd) (b) (3 points) Using right-hand Riemann sums, approximate R as a function of d. That is, fill out the following table d (m) R (10' bacteria/s) 0 0.5 1 1.5 2 2.5 3 3.5 4 (c) (2 points) Extremophiles can only exist a particular distance away from a geothermal vent depending on the temperature of the vent. We can model this by assuming that all extremophiles exist a distance d = -0.00472 + 3.4T - 719 from the centre of the vent, where T is the temperature of the vent in units of C and varies between 400 C and 450 C. Modify your expression in (a) to give the rate of reproduction R as a function of T. (d) (3 points) Given that it's quite easy to measure the temperature of a vent remotely, we can use part (c) to find our ideal vent to send missions. Find the temperature T which maximizes the rate of reproduction of extremophiles. A useful quantity for our purposes is the reproductive distance rate F of a geothermal vent. This measures how much the extremophiles reproduce per metre from the centre of the geothermal vent and has units of 104 bacteria per metre times seconds. For a generic vent, the distance rate F has been measured to give the following table. 1 1.5 2 2.5 3 3.5 4 0.2 -0.3 -0.8 -1.2 distance from vent (m) 0 0.5 F (10 bacteria/ms) 0 0.5 0.78 1 1.2 (a) (2 points) Write down (but do not evaluate!) an integral expression for the rate R at which extremophiles reproduce a given distance d away from the centre of the geothermal vent provided you know the rate of reproduction is 0 at the centre of the geothermal vent. (Hint: R has units 104 bacteria/s) (Hint: if I was constant, then R = Fd) (b) (3 points) Using right-hand Riemann sums, approximate R as a function of d. That is, fill out the following table d (m) R (10' bacteria/s) 0 0.5 1 1.5 2 2.5 3 3.5 4 (c) (2 points) Extremophiles can only exist a particular distance away from a geothermal vent depending on the temperature of the vent. We can model this by assuming that all extremophiles exist a distance d = -0.00472 + 3.4T - 719 from the centre of the vent, where T is the temperature of the vent in units of C and varies between 400 C and 450 C. Modify your expression in (a) to give the rate of reproduction R as a function of T. (d) (3 points) Given that it's quite easy to measure the temperature of a vent remotely, we can use part (c) to find our ideal vent to send missions. Find the temperature T which maximizes the rate of reproduction of extremophiles.
Expert Answer:
Answer rating: 100% (QA)
a The integral expression for the rate R at which extremophiles reproduc... View the full answer
Related Book For
Cost Accounting A Managerial Emphasis
ISBN: 978-0133392883
6th Canadian edition
Authors: Horngren, Srikant Datar, George Foster, Madhav Rajan, Christ
Posted Date:
Students also viewed these mathematics questions
-
List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Abbie Young is the manager of the customer-service division of an electrical appliance store. Abbie is considering buying a machine at a cost of $10,000 on December 31, 2019. The machine will last...
-
Reconsider your assessed 0.05 and 0.95 fractiles in Problem 8.13.If you are perfectly calibrated when judging these fractiles, then you would expect that in any given situation the actual value has a...
-
Suppose you buy a house for $150,000. One year later, the market price of the house has risen to $165,000. What is the return on your investment in the house if you made a down payment of 20 percent...
-
The influence of temperature on the equilibrium constant of a chemical reaction can be obtained from (a) \(\left(\frac{\partial \ln K}{\partial T} ight)=-\frac{\Delta \dot{H}}{T^{2}}\) (b) \(\ln...
-
Two adjusting entries are in the following general journal. Post these adjusting entries to the four general ledger accounts. The following account numbers were taken from the chart of accounts: 141,...
-
Let Timco use a capital structure that is 30% debt and 70% equity, The firm can borrow at 5%. The tax rate is 40%. Let the firm beta be 1.5, the market return 14%, and the risk free rate 2%. Find the...
-
Imagine that you have 10,000 to invest. What would be the combination of Asset A and Asset B that would yield you an expected return of 4%? What is the standard deviation of the portfolio described...
-
Describe the graphing method for solving a system of equations.
-
Describe a procedure for using the inverse of a matrix to solve a system of equations.
-
Show that the equation of a line passing through \((h, k)\) with slope \(m\) is \[y-k=m(x-h)\] This is called the point-slope form.
-
Describe the process for adding matrices.
-
In Problems 1-5, perform the indicated matrix operations, if possible, where \[\begin{array}{ll}{[\mathrm{A}]=\left[\begin{array}{rr}1 & 0 \\2 & -1\end{array}ight]} &...
-
Integration is a vital concept when applied in one?s life. Integrating your life means making ideal choices. Perfect choices on the other go in line with quality decisions. Quality decisions lead to...
-
As economic conditions change, how do banks adjust their asset portfolio?
-
How would each of the following liabilities be classified (current, non-current, or both) at the end of the financial year? Unearned revenue Accrued expenses Provision for warranty repair costs...
-
The following were among transactions of Everluck Enterprises Ltd during the financial years ending 30 June 2023 and 30 June 2024. Required Record in general journal form all the above transactions,...
-
At 30 June 2024, the accountant for Woodbine Construction, Mary Ellam, is preparing the financial statements for the year ended on that date. To calculate the annual leave payable, the accountant had...
Study smarter with the SolutionInn App