As mentioned in the previous answer, an expression for the amount of pumpkin pie, p(t), as a function of time, t, using an exponential function is:
p(t) = p_0 e^(-kt)
where:
- p_0 is the initial amount of pumpkin pie at time t = 0
- k is the decay rate constant, which determines how quickly the pumpkin pie decays over time
- e is the mathematical constant equal to approximately 2.71828, the base of the natural logarithm
To illustrate the use of the exponential function, we can work through an example:
Suppose that the initial amount of pumpkin pie is 1000 grams, and the decay rate constant is k = 0.01 per minute. We can write the expression for the amount of pumpkin pie as:
p(t) = 1000 e^(-0.01t)
To evaluate the amount of pumpkin pie, p(t), after 30 minutes, we substitute t = 30 into the equation:
p(30) = 1000 e^(-0.01*30)
p(30) = 740.82 grams
This means that after 30 minutes, the amount of pumpkin pie remaining is approximately 740.82 grams.
