The document discusses an exponential model equation used to model virus growth over time. It shows how to derive a new exponential model based on an original model when the rate of growth decreases by 80%. The new model is then used to calculate the total amount of virus infected cells after 8 hours, given the initial amount from the original model.

1. Annotation 3 Viruses

2. Slide 1 This Equation is an Exponential Model equation. “A” represents the amount at the end of the time period, “Ao” represents the initial amount, “m” is an exponential model of growth/decay, and “t” represents the time it takes from “Ao” to “A.” We substitute the values given into our equation. Simplifying occurs. We use the Natural Logarithm making each term an exponent with base “e,” a constant. (Remember, logarithms are exponents) We bring down the 3 using the Law of Logarithms: More simplifying occurs and results with the model from 2000-2240 in 3 hours.

3. Slide 2 We simply calculate the approximate value of our model. Comparing and the compound interest equation (P = Ao), we notice that they are based on the same idea except that the compound interest has the variable “n” which represents the number of compounding periods during one time period. In our Exponential model, the value of “n” is still present with a value of 1 (1 compound per time period). So in conclusion, we can state that (1+r) = m. We find the rate of the old model by subtracting 1. Since the rate of growth is decreased by 80%, the rate of growth is increasing only at a rate of 20% (r x 0.20) Adding 1 back to the new rate gives us our new model

4. Slide 3 Now that we have the new model of growth, we re input it back into the Exponential Model equation with an initial amount of virus infected cells of 2240. Solving through for A gives us the total amount of virus infected cells after the next 8 hours.