Chapter 12.5, Problem 53E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Tumor volume Let V denote the volume of a tumor and suppose that the growth rate of the tumor satisfies d V d t = 0.2 V e − 0.1 t If the initial volume of the tumor is 1.86 units, find an equation for V as a function of t.

To determine

To calculate: The equation for the volume of the tumor as a function of time t where the growth rate of the tumor is given as, dVdt=0.2Ve0.1t where V is the volume of the tumor.

Explanation

Given information:

The growth rate of the tumor is given as, dVdt=0.2Ve0.1t and the initial volume of the tumor is 1.86 units.

Formula used:

The logarithmic rule of integrals, 1xdx=ln|x|+C where x0.

The natural logarithm property,

logab=yb=ay.

Calculation:

Consider the growth rate of the tumor, dVdt=0.2Ve0.1t.

Rewrite the above differential equation,

dVV=0.2e0.1tdt

Integrate both side of the equation as:

dVV=0.2e0.1tdt

Now, use the logarithmic rule of integrals to get,

dVV=0.2e0.1tdtlnV=0.2e0.1t0

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