Question

The initial viral count in blood drawn from a patient is 10,000 particles per ml. Five hours later the viral count is 15,000 particles per ml.

A)Find a specific function of the form m(t)=n0e^kt, to model the number of virus particles per ml as a function of time

Answer 1

The function to model the number of virus particles per ml as a function of time is m(t) = 10,000e^(ln(1.5)/5)t, where n0 = 10,000 is the initial amount, and t is time in hours.

Step-by-step explanation:

The student is asking for a specific exponential function to model the number of virus particles per ml as a function of time. The form m(t)=n0ekt is an exponential model where n0 is the initial amount, k is the growth rate, and t is time. Initially, we have n0 = 10,000 particles per ml. After t = 5 hours, m(5) = 15,000 particles per ml. We need to find the value of k.

To find k, we use the given data:

15,000 = 10,000e5k

Dividing both sides by 10,000, we get:

1.5 = e5k

Now we take the natural logarithm:

ln(1.5) = 5k ln(e)

ln(1.5) = 5k

\(k = \frac{ln(1.5)}{5}\)

Once k is calculated, we can write the specific function that models the number of virus particles per ml over time as:

m(t) = 10,000e\(\frac{ln(1.5)}{5}\)t