1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
umka2103 [35]
3 years ago
13

A model for tumor growth is given by the Gompertz equation dV dt = a (In b-, In V) V where a >0 and b >0 are constants and

V is the volume of the tumor measured in mm3 Find the solution for tumor volume as a function of time that has an initial tumor volume of V(0) 1 mm3.
Mathematics
1 answer:
Xelga [282]3 years ago
5 0

Answer:

V(t) = b^{(1-e^{-at})}

Step-by-step explanation:

We are given the following information in the question:

\displaystyle\frac{dV}{dt} = a (In b - In V) V

where a > 0 and b > 0.

\displaystyle\frac{dV}{dt} = a (In b-In V) V\\\\\displaystyle\frac{dV}{dt} = -aV(ln\frac{V}{b})\\\\\frac{dV}{V(ln\frac{V}{b})} = (-a)dt\\\\\text{Put } ln\frac{V}{b} = z\\\\\text{Integrating both sides}\\\\\int \frac{dV}{V(ln\frac{V}{b})} = \int (-a)dt\\\\\text{We get}\\\\\int \frac{dz}{z} = \int (-a)dt\\\\\\\text{where C is the constant of integration}

V(0) = 1~ mm^3\\V(t) = b.e^{e^{-at+C}}\\\text{Putting t =0, V(0) = 1}\\\\V(0) = 1 = b.e^{e^{C}}\\\\V(t) = b^{(1-e^{-at})}

where v(t) is the required tumor volume as a function of time that has an initial tumor volume of V(0) = 1 cubic mm.

You might be interested in
What is (7x-5)- (3x-2)
BaLLatris [955]

Answer:

4x-3

Step-by-step explanation:

Multiply the minus sign to lose the brackets

7x-5-3x+2

combine like terms

7x-3x-5+2

Simplify

4x-3 Answer

Hope this helps!

8 0
3 years ago
(10 + 3) - (20 ÷ 10)​ 2​ )
Paul [167]

I believe the answer is 9.

5 0
3 years ago
A 5 pound bag of apples costs 4.50 and an 8 pound bag of the same type of apples costs 7.52 greg found the unit price which is t
irga5000 [103]

Answer: 0.04 per pound

Step-by-step explanation:

A 5 pound bag of apples costs 4.50.

The unit price will be 4.50 divided by 5 which will be:

4.50 ÷ 5 = 0.9

The unit price is 0.9 per pound

A 8 pound bag of the same type of apples costs 7.52.

The unit price will be 7.52 divided by 8 which will give:

7.52 ÷ 8 = 0.94

The unit price is 0.94 per pound

The difference in the unit prices will be the subtraction of 0.90 from 0.94.

0.94 - 0.90 = 0.04

The difference in the unit prices is 0.04 per pound.

6 0
3 years ago
Determine the value of y, if x is 5.<br> y = x2-7
lions [1.4K]

Answer:

Y = 3

Step-by-step explanation:

5 times 2 is 10 minus 7 is 3.

5 0
3 years ago
Read 2 more answers
Evaluate the expression 2 + 23 × 5 - 3
insens350 [35]
Answer: 2+23x5-3
 
        =    2 + 115 -3
     
        =   117 - 3
 
        = 114



6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the difference 32.654 -0.1
    11·2 answers
  • PLEASE HURRY!!
    12·1 answer
  • Practice Q:If I am 13 and I was born in 2003,and my brother was born in 2006,then how old is he?
    7·2 answers
  • Which term describes a fraction that has a polynomial in its numerator and its denominator?
    9·2 answers
  • How do I multiply 12.8 x 3/4 as a fraction.​
    9·1 answer
  • What value of a will make the following equation true?
    14·1 answer
  • Sophia had 63¢ until she spent 5 nickels. How much money does Sophia have now?
    14·2 answers
  • A 3-yard roll of wrapping paper costs $13.14. What is the price per foot?​
    8·1 answer
  • Pls show work and solve :( , I give brainliest to 1st right answer
    13·1 answer
  • Please Help!!!!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!