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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)=

The country of Sylvania has decided to reduce the number of its illiterate citizens by 35 \frac{3}{5} each year. This year there are 90009000 illiterate people in the country.\newlineWrite a function that gives the number of illiterate people in Sylvania, P(t) P(t) , t t years from today.\newlineP(t)=□ P(t)=\square

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Q. The country of Sylvania has decided to reduce the number of its illiterate citizens by 35 \frac{3}{5} each year. This year there are 90009000 illiterate people in the country.\newlineWrite a function that gives the number of illiterate people in Sylvania, P(t) P(t) , t t years from today.\newlineP(t)=□ P(t)=\square
  1. Understand Reduction Fraction: Step 11: To model the reduction in the number of illiterate people, we need to understand that reducing the population by (3)/(5)(3)/(5) means that each year, (2)/(5)(2)/(5) of the population remains. This is because 1−(3)/(5)=(2)/(5)1 - (3)/(5) = (2)/(5).
  2. Initial Population Value: Step 22: The initial number of illiterate people is given as 90009000. This will be our starting value for the function P(t)P(t).
  3. Calculate Annual Multiplier: Step 33: Since the population is reduced by (35)(\frac{3}{5}) each year, the remaining fraction, (25)(\frac{2}{5}), will be our annual multiplier. This means that each year, the population is multiplied by (25)(\frac{2}{5}) to find the new number of illiterate people.
  4. Write Function P(t): Step 44: We can now write the function P(t)P(t) that models the number of illiterate people after tt years. The function will have the form P(t)=initial value×(annual multiplier)tP(t) = \text{initial value} \times (\text{annual multiplier})^t. Substituting the given values, we get P(t)=9000×(25)tP(t) = 9000 \times \left(\frac{2}{5}\right)^t.
  5. Check Function for Accuracy: Step 55: To check if the function is correct, we can consider what happens after 11 year. P(1)P(1) should be 9000×(25)1=9000×25=36009000 \times \left(\frac{2}{5}\right)^1 = 9000 \times \frac{2}{5} = 3600, which is the expected number of illiterate people after a reduction of 35\frac{3}{5}.

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