Answer:
Approximately 459.17 hours.
Step-by-step explanation:
To determine how long it will take for the mold to completely cover the apple, we need to calculate the number of hours it will take for the mold to grow from covering 1% to 100% of the apple's surface area.
Let's break down the problem step by step:
1. Initially, the mold covers 1% of the apple's surface area, which means 99% of the surface area is still mold-free.
2. The mold expands at a rate of 10% per hour. This means that every hour, the mold will cover an additional 10% of the remaining mold-free surface area.
3. We can calculate the number of hours it will take for the mold to cover 99% of the surface area (since it starts with 1% coverage and needs to reach 100% coverage).
To do this, we can set up an equation:
0.99^n = 0.01
Here, 'n' represents the number of hours it will take for the mold to cover 99% of the surface area.
Taking the logarithm (base 0.99) of both sides of the equation, we can solve for 'n':
n = log(0.01) / log(0.99)
Using a calculator, we find that n is approximately 459.17 hours.
Therefore, it will take approximately 459.17 hours for the mold to completely cover the apple's surface area.
