The half-life of an antibiotic in the bloodstream is 10 hours. If an initial dose of 20

Question:

The half-life of an antibiotic in the bloodstream is 10 hours. If an initial dose of 20 milligrams is administered, the quantity left after t hours is modeled by Q(t) = 20e^-0.0693t, for t ≥ 0.

a. Find the instantaneous rate of change of the amount of antibiotic in the bloodstream, for t ≥ 0.

b. How fast is the amount of antibiotic changing at t = 0? At t = 2?

c. Evaluate and interpret

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Feb 08, 2019 12:06 PM

See More Questions

The half-life of palladium-100, 100Pd, is four days. (So half of any given quantity of 100Pd will disintegrate in four days) The initial mass of a sample is one gram. (a) Find the mass that remains...
The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by (a) For what t-values is x increasing? (b) Find the t-value at which x is maximum. (c)...
Determine the half-life of the radioactive substance described in Problem 6. Data from problem 6 Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased...
The registers values in AX and BX can be exchanged using stack operations that are: Select one: a. PUSH bx PUSH ax POP bx POP AX b. none C. PUSH ax PUSH bx POP ax POP bx d. PUSH ax POP ax PUSH bx POP...
Bassing Corp. uses a periodic inventory system and reports the following information: sales $750,000; sales returns and allowances $75,000; sales discounts $25,000; purchases $425,000; purchase...
Write an article in which describe the "Effects of Exercise Training on Hippocampal Volume in Humans.
Use Table XV in Appendix B to find the values of 4 and D, for each of the following sample sizes. a.n=4 b.n=12 c.n=24
Halsey Company sells women's clothing. Halsey's strategy is to offer a wide selection of clothes and excellent customer service and to charge a premium price. Halsey presents the following data for...
Question 10 of 50
A manufacturer is considering alternatives for building new plants, to be located closer to three of its primary customers with whom it intends to develop long-term, sole-supplier relationships. The...
Consider the following population functions. a. Find the instantaneous growth rate of the population, for t 0. b. What is the instantaneous growth rate at t = 5? c. Estimate the time when the...
A $200 investment in a savings account grows according to A(t) = 200e 0.0398t , for t 0, where t is measured in years. a. Find the balance of the account after 10 years. b. How fast is the account...
The V-shaped tank has width w into the paper and is filled from the inlet pipe at volume flow Q. Derive expressions for (a) the rate of change dh/dt and (b) the time required for the surface to rise...
PP Company purchases a material that is then processed to yield three chemicals: anarol, estyl, and betryl.In June, PPC purchased 10,000 gallons of the material at a cost of $250,000, and the company...
Suppose Boyson Inc. free cash flow for the next year is $ 1 5 0 , 0 0 0 and the FCF is expected to grow a concert rate of 6 . 5 % if WACC is 1 2 . 5 % what is the market value of the firm?
An eight lane urban freeway (four lanes in each direction) is on rolling terrain and has 11-ft lanes with a 4-ft right-side shoulder. The interchange density is 1.25 per mile. The base free-flow...
For the following business events, please indicate the increase (+) or decrease (-) on the following income statement and balance sheet categories. If there is no effect, leave the box blank. If...
4. Change the magnet to the original orientation and drag through the coil. a. What happens to the voltage and light bulb as the North Pole moves through the coil? b. What happens to the voltage and...
The hyperfine coupling constant in CH 3 is 2.3mT. Use the information in Table 14D.1 to predict the splitting between the hyperfine lines of the spectrum of CD 3 . What are the overall widths of the...
PC Contractors, Inc., was an excavating business in Kansas City, Missouri. Union Bank made loans to PC, subject to a perfected security interest in its equipment and other assets, including...
Use either a computer algebra system or a table of integrals to find the exact length of the arc of the curve y = e x that lies between the points (0, 1) and (2, e 2 ).
For the function f (x) = 1/4 e x + e -x , prove that the arc length on any interval has the same value as the area under the curve.
Find the length of the curve y= 1 < x < 4 Vt3 1 dt
44. Dryer Companys policy is to keep 25% of the next month's sales in ending inventory. If Dryer meets its ending inventory policy at the end of April and sales are expected to be 24,000 units in May...
What general conclusions can you draw about your companys liquidity, solvency and productivity based on your ratio calculations. Working Capital 2017 = $9,994 M 2016 = $10,673 M Current Ratio 2017 =...
Tami Tyler opened Tami's Creations, Incorporated, a small manufacturing company, at the beginning of the year. Getting the company through its first quarter of operations placed a considerable strain...

The half-life of an antibiotic in the bloodstream is 10 hours. If an initial dose of 20

Question:

lim Q(t) and lim Q'(t).

Step by Step Answer:

a The instantaneous rate of change is Qt 1386e 00693t mghr b At t 0 hours we have Q0 13...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions