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Warm-Up 1.3.2 Day 5

Warm-Up 1.3.2 Day 5.

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Warm-Up 1.3.2 Day 5

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  1. Warm-Up 1.3.2 Day 5 This year, Zachary has been babysitting his young cousins after school for $70 a month. His uncle also gave him an extra bonus of $100 for his hard work. Since school started, Zachary has earned more than $500. How many months ago did school start? Write an inequality that represents this situation. Solve it and show all work. So school started more than 5 months ago.

  2. Key Concepts • The general form of an exponential equation is , where a is the initial value, b is the base, and x is the time. The final output value will be y. • b must always be greater than zero. • If the base is greater than 1 (b > 1), then the equation models exponential growth. • If the base is between 0 and 1 (0 < b < 1), then the exponential equation represents exponential decay.

  3. Additional Hints! • Look for words such as double, triple, half, or quarter. These words give the number of the base. • Look for words like initial or starting to substitute for a.

  4. Example 1 • A population of mice quadruples every year. If a mouse nest started out with 2 mice, how many mice would there be after 4 years? Write an equation and then use it to solve the problem. • First, make a list of what we know. • Then, write your equation. Base = quad which means 4, so b= 4 X = every 6 months for 2 years so 4 times during that time Initial mice = 2 So a = 2 512 mice after 2 years

  5. Example 2 • In sporting tournaments, teams are eliminated after they lose. The number of teams in the tournament then decreases by half with each round. If there are 16 teams left after 3 rounds, how many teams started out in the tournament? • First, make a list of what we know. • Then, write your equation. Final number = 16 Reduction = ½ Time = 3 128 teams started out in the tournament.

  6. Key Concept • Sometimes, values may increase after different time periods. For instance, Example 1 tells us that the population of mice increases every ONE year. What if we were told that the population of mice quadrupled every 2 years? • We can take this information and tweak our formula slightly to represent this time interval:  where 2 represents every 2 years.

  7. Example 3 • The number of roses that bloom on your rosebush doubles every 4 days. If the rose bush began with 5 blooms, how many roses would there be after 20 days? • First, make a list of what we know. • Then, write your equation. Initial number= 5 Doubles every 4days Time period is 20 days The rose bush will have 160 blooms after 20 days.

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