Question

It is usually not a good idea to let the microwave oven run until all the kernels are popped because some of the popcorn will start to burn. Suppose the ideal time to shut off the microwave oven is after about 97.5% of the kernels have popped. When will 97.5% of the kernels be popped?

Answer 1

To determine when 97.5% of the popcorn kernels will be popped, we can use the concept of exponential decay. We can use a mathematical equation to calculate the number of runs it will take for 97.5% of the kernels to be popped. Plugging in the given values, we can find the answer.

Step-by-step explanation:

In order to determine when 97.5% of the popcorn kernels will be popped, we need to understand the concept of exponential decay. Every time the microwave runs, a certain percentage of the unpopped kernels will pop. Let's assume that each time the microwave runs, 90% of the remaining unpopped kernels will pop. So, after the first run, 10% will remain unpopped. After the second run, 10% of the remaining 10% will remain unpopped, which is 1%. This pattern continues until we reach 97.5% remaining unpopped kernels.

We can represent this mathematically using the equation:

p = p0(1 - r)n

where p is the percentage of unpopped kernels remaining, p0 is the initial percentage of unpopped kernels, r is the ratio of popped kernels in each run, and n is the number of runs. Rearranging the equation to solve for n, we get:

n = log(1 - r)(p / p0)

Plugging in the given values, with p0 = 100%, p = 2.5%, and r = 10%, we can calculate the value of n.