Concept explainers
Cancer cells grow exponentially with a doubling time of 20 h when they have an unlimited nutrient supply. However, as the cells start to form a solid spherical tumor without a blood supply, growth at the center of the tumor becomes limited, and eventually cells start to die.
(a) Exponential growth of cell number N can be expressed as shown, where
(b) Write an equation that will describe the rate of change of tumor volume during exponential growth given that the diameter of an individual cell is 20 microns.
(c) After a particular type of tumor exceeds 500 microns in diameter, the cells at the center of the tumor die (but continue to take up space in the tumor). Determine how long it will take for the tumor to exceed this critical size.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Additional Engineering Textbook Solutions
Fundamentals of Differential Equations (9th Edition)
Advanced Engineering Mathematics
Basic Technical Mathematics
Elementary Statistics (Text Only)
- Newton's second law of motion leads to: the rate of change of linear momentum is equal to the applied moment the rate of change of linear momentum is equal to the applied force the rate of change of angular momentum is equal to the applied force the mass times acceleration of a particle is equal to the applied forcearrow_forwardCopra enters a dryer containing 60% water and 40% of solids leaves with 5% water and 95% solids. Find the weight of water removed based on each pound of original product. Answer: weight of water removed = 0.58 lbarrow_forwardGive True or False for the following: 1.In liquids and gases, heat transmission is caused by conduction and convection 2.The surface geometry is the important factor in convection heat transfer 3. The heat transfer by conduction from heated surface to the adjacent layer of fluid, 4. The heat transfer is increased in the fin when &> 1 5.The unit of the thermal diffusivity is m²/s 6. Temperature change between the materials interfaces is attributed to the thermal contact resistance 7. A material that has a low heat capacity will have a large thermal diffusivity. 8. Heat conduction flowing from one side to other depends directly on thickness 9.Fin efficiency is the ratio of the fin heat dissipation with that of no fin 10.The critical radius is represented the ratio of the convicted heat transfer to the thermal conductivityarrow_forward
- 1. In general, the internal energy U depends on both temperature and volume, U=U(TV). The volume dependence comes from the potential energy due to the interactions among the particles. For free particles, there are no interactions, thus, the internal energy U should be independent of the volume, i.e., = 0. Verify this result for ideal gas pV = RT. au avarrow_forwardThe elastic potential energy of a spring Ve depends on the spring constant k of the spring and the extension of the spring according to: O V. = kx. O Ve = – kx. O Ve = kx. O Ve = kx.arrow_forwardOn average, a pair of running shoes can last 18 months if used every day. The length of time running shoes last is exponentially distributed. What is the probability that a pair of running shoes last more than 15 months? Eighty percent of running shoes last at most how long if used every day?arrow_forward
- Two kinds of bacteria are found in a sample of tainted food. It is found that the population size of type 1, N1 and of type 2, N2 satisfy the equation dN/dt=-0.1/N1 dN/dt30.7/N2 N1 is equal to 1000 at time equal to zero, while N2 is equal to 30 at time equal to zero. Then the population sizes are equal N1 = N2 at what time? (4 decimal places)arrow_forwardThe left side of this equation tells how much energy Q the cylinder gives to the water while it cools. The right side of this equation tells how much energy Q the water and aluminum cup absorb from the cylinder to warm up. Because it is the same energy, they are equal. What is known in this equation? Mcyl 411.7 g, malum 46.5 g, malum+water = 175 g Can you find: mwater =? g Twater = Talum = 20°C (water and cup of room temperature) 90°C, T; = 35°C (hot cylinder and cool "cylinder+cup+water" temperatures) Tcyl kCal Calum = 0.22, Cwater 1 (specific heat of water and aluminum, measured in units kg-°C What are we looking for is Ccul - How we find it? Plug all the numbers into the equation (1), Ccul will be one unknown which you can calculate from the equation. Important, convert all the masses from grams to kilograms! After you find Ccyl, compare it to known value for the copper 0.093(our cylinder is made out of copper). |Ceyl -0.093| % : · 100% 0.093arrow_forwardOne mole of a gas obeys the Ideal Gas Law PV = 20T, where P is pressure, V is volume, and T is temperature. If the temperature T of the gas is increasing at the rate of 5 °C/s and if, when the temperature is 80 °C, the pressure P is 10N/m? and is decreasing at the rate of 2- find the m2 . s rate of change of the volume V with respect to time.arrow_forward
- A closed thermodynamic system consists of a fixed amount of substance (i.e. mass) in which no substance can flow across the boundary, but energy can. For a closed themodynamic system we cannot add energy to the system, via substance (E ) (1.e. matter which contains energy is not allowed across the boundary) Across the Boundaries E° = No Q = = Yes W mass NO CLOSED = Yes SY STEM m = constant | energy YES Figure 1.1. If the substance inside the thermodynamic system shown in figure 1.1. (i.e. piston cylinder device) is air, is the system a Fixed closed system Moveable closed system A. В.arrow_forward2. A tank initially holds 100 gal of a brine solution containing 20 lb of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min, while the well-stirred mixture leaves the tank at the same rate. Find the amount of salt x in the tank (in lbs) at any time t (in minutes). A) x = 20e 20 В) х%3D 20е 10 С) х%3D 20е D) x= 20earrow_forwardSuppose a hippopotamus on land receives 73 units of heat per minute due to solar radiation and 52 units of heat per minute due to infrared radiation. It emits 39 units of infrared radiation and it loses 66 units heat per minute through evaporation. The hippopotamus gains 45 units of heat per minute through its metabolism. Overall, its heat energy is increasing by 50 units per minute (i.e. its temperature is increasing). Delta Hanimal = SR + IRin - IRout ± Hconv ± Hcond - Hevap + Hmet Based on this information we can conclude that the combination of conduction and convection is the animal, and that its current temperature is than the ambient temperature. Select one: a. cooling; warmer b. warming; warmer c. cooling; cooler d. warming; coolerarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning