Final answer:
To reduce the number of cases from 10,000 to 1000, it will take approximately 6 years if the number of cases is reduced by 20% each year.
Step-by-step explanation:
To find out how many years it will take to reduce the number of cases to 1000, we need to calculate the percentage decrease in cases per year. If the number of cases is reduced by 20% each year, then the number of cases in the next year is 80% of the previous year. We can set up the following equation: 10000 * 0.8^n = 1000, where n is the number of years it takes to reduce the cases to 1000.
We can solve for n by taking the logarithm of both sides of the equation:
log(10000 * 0.8^n) = log(1000)
log(10000) + log(0.8^n) = log(1000)
log(10000) + n * log(0.8) = log(1000)
n * log(0.8) = log(1000) - log(10000)
n = (log(1000) - log(10000)) / log(0.8)
n is approximately equal to 5.95 years. Therefore, it will take approximately 6 years to reduce the number of cases to 1000.