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) 2,129.520
B) 2,099.520
C) 2,049.520
D) 491.383
E) 262,440.000

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) 2,129.520 
B) 2,099.520 
C) 2,049.520 
D) 491.383 
E) 262,440.000

Quizplus · Accepted Answer

The general formula for exponential growth or decay is:

N = N0 * e^(kt)

Where N0 is the initial value of N, k is the proportionality constant, and t is time.

We can use the given information to set up a system of equations:

N1 = N0 * e^(k*t1)
N2 = N0 * e^(k*t2)

Dividing the two equations, we get:

N2/N1 = e^(k*(t2-t1))

Solving for k, we have:

k = ln(N2/N1)/(t2-t1)

Substituting the values given in the problem, we have:

k = ln( 56962592 / 43046721 ) / ( 3 - 2 )

k ≈ 0.2731

Using the given value of t3 = 6, we can find N3:

N3 = N0 * e^(k*t3)

N3 = 43046721 * e^(0.2731*6)

N3 ≈ 2099.52

Therefore, the answer is B) 2,099.520

The Rate of Change of N Is Proportional to N