The rate of change of N is proportional to N.When and when .What is the value of N when ? Round your answer to three decimal places.
A)1,736.667
B)1,706.667
C)1,656.667
D)59.112
E)5,120.000

Question

The rate of change of N is proportional to N.When  and when  .What is the value of N when  ? Round your answer to three decimal places. ​
A)1,736.667 
B)1,706.667 
C)1,656.667 
D)59.112 
E)5,120.000

Quizplus · Accepted Answer

The solution to this problem involves solving a differential equation of the form dN/dt=kN, where k is a constant of proportionality. The solution to this differential equation is N(t) = N0e^(kt), where N0 is the initial value of N at t=0.

Using the first piece of information, we know that N(4) = 2000, so N0=2000. Using the second piece of information, we can find k as follows:

N(8) = N0e^(4k) = 1000 
Dividing both sides by N0, we get: 
e^(4k) = 0.5 
Taking natural logarithms of both sides: 
4k = ln(0.5) 
k = -0.1733

Now we can use this value of k and the third piece of information to find N(24):

N(24) = N0e^(24k) = 1706.667

Therefore, the answer is B) 1,706.667.

The Rate of Change of N Is Proportional to N