Question

After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining is modeled by the function B(t) = 8500⋅(8/27)^t^3. Complete the sentence about the rate of change of the number of bacteria.

Answer 1

The rate of change of the number of bacteria can be calculated by finding the derivative of the function B(t) = 8500⋅(8/27)^t^3 with respect to time, t.

Step-by-step explanation:

The rate of change of the number of bacteria can be calculated by finding the derivative of the function B(t) = 8500⋅(8/27)^t^3 with respect to time, t. The derivative represents the rate at which the number of bacteria is changing at a given time. To find the derivative, we can use the power rule: d/dt (a^t) = ln(a) * a^t. Applying the power rule to B(t) = 8500⋅(8/27)^t^3 gives us the derivative d/dt (B(t)) = ln(8/27) * 3t^2 * (8/27)^t^3.