The country of Sylvania has decided to reduce the number of its illiterate citizens by (3)/(5) each year. This year there are 9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania, P(t),t years from today. P(t)=

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The country of Sylvania has decided to reduce the number of its illiterate citizens by  (3)/(5) each year. This year there are 9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania,  P(t),t years from today.  P(t)=

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Understand Reduction Fraction:  Step 1: To model the reduction in the number of illiterate people, we need to understand that reducing the population by (3)/(5) means that each year, (2)/(5) of the population remains. This is because 1 - (3)/(5) = (2)/(5). Initial Population Value:  Step 2: The initial number of illiterate people is given as 9000. This will be our starting value for the function P(t). Calculate Annual Multiplier:  Step 3: Since the population is reduced by (3)/(5) each year, the remaining fraction, (2)/(5), will be our annual multiplier. This means that each year, the population is multiplied by (2)/(5) to find the new number of illiterate people. Write Function P(t):  Step 4: We can now write the function P(t) that models the number of illiterate people after t years. The function will have the form P(t) = initial value * (annual multiplier)^t. Substituting the given values, we get P(t) = 9000 * ((2)/(5))^t. Check Function for Accuracy:  Step 5: To check if the function is correct, we can consider what happens after 1 year. P(1) should be 9000 * ((2)/(5))^1 = 9000 * (2)/(5) = 3600, which is the expected number of illiterate people after a reduction of (3)/(5).

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