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1. 5 –2

1. ANSWER. 2. 25. 3. 2. 8. 4. ANSWER. Evaluate the expression without using a calculator. 1. 5 –2. 3. –3 4. ANSWER. –24. 3. 2. domain: all real numbers; range: y ≤ 3. ANSWER. Evaluate the expression without using a calculator.

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1. 5 –2

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  1. 1 ANSWER 2 25 3 2. 8 4 ANSWER Evaluate the expression without using a calculator. 1. 5–2

  2. 3. –3 4 ANSWER –24 3 2 domain: all real numbers; range: y ≤ 3 ANSWER Evaluate the expression without using a calculator. 4.State the domain and range of the function y = –(x – 2)2 + 3.

  3. x 2 Graph y = . x EXAMPLE 1 Graph y=b for b > 1 SOLUTION STEP 1 Make a table of values. STEP 2 Plot the points from the table. Draw, from left to right, a smooth curve that begins just above the x-axis, passes through the plotted points, and moves up to the right. STEP 3

  4. x a.y = 4 x 1 1 Graph y = ab for b > 1 a. Plot and (1, 2) .Then, from left to right, draw a curve that begins just above the x-axis, passes through the two points, and moves up to the right. 2 2 0, EXAMPLE 2 Graph the function. SOLUTION

  5. 1,– x b. y = – x 5 5 Graph y = ab for b > 1 b. 2 2 Plot (0, –1) and . Then,from left to right, draw a curve that begins just below the x-axis, passes through the two points,and moves down to the right. EXAMPLE 2 Graph the function. SOLUTION

  6. x– 1 Graphy = 4 2 – 3.State the domain and range. Begin by sketching the graph of y = 4 2 , which passes through (0, 4) and (1, 8). Then translate the graph right 1 unit and down 3 units to obtain the graph of y = 4 2 – 3.The graph’s asymptote is the line y = –3. The domain is all real numbers, and the range is y > –3. x x–h Graph y = ab + k for b > 1 x– 1 EXAMPLE 3 SOLUTION

  7. x 1. y = 4 for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. State the domain and range.

  8. x 2. y = 3 2 3 for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. State the domain and range.

  9. x + 1 3. f (x) = 3 + 2 for Examples 1, 2 and 3 GUIDED PRACTICE Graph the function. State the domain and range.

  10. In 1996, there were 2573 computer viruses and other computer security incidents. During the next 7 years, the number of incidents increased by about 92% each year. Computers EXAMPLE 4 Solve a multi-step problem • Write an exponential growth model giving the number n of incidents tyears after 1996. About how many incidents were there in 2003?

  11. t t = 2573(1.92) n = a(1 + r) t = 2573(1 + 0.92) EXAMPLE 4 Solve a multi-step problem • Graph the model. • Use the graph to estimate the year when there were about 125,000 computer security incidents. SOLUTION STEP 1 The initial amount is a = 2573 and the percent increase is r =0.92. So, the exponential growth model is: Write exponential growth model. Substitute 2573 for aand 0.92 for r. Simplify.

  12. Using this model, you can estimate the number of incidents in 2003 (t = 7) to be n = 2573(1.92) 247,485. 7 EXAMPLE 4 Solve a multi-step problem STEP 2 The graph passes through the points (0, 2573) and (1,4940.16). Plot a few other points. Then draw a smooth curve through the points.

  13. Using the graph, you can estimate that the number of incidents was about 125,000 during 2002 (t 6). EXAMPLE 4 Solve a multi-step problem STEP 3

  14. for Example 4 GUIDED PRACTICE 4.What If?In Example 4, estimate the year in which there were about 250,000 computer security incidents. SOLUTION 2003

  15. x 5.In the exponential growth model y = 527(1.39) , identify the initial amount,the growth factor, and the percent increase. for Example 4 GUIDED PRACTICE SOLUTION Initial amount: 527Growth factor 1.39Percent increase 39%

  16. FINANCE You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 1 year if the interest is compounded with the given frequency. EXAMPLE 5 Find the balance in an account a.Quarterly b.Daily

  17. = 4000 1 + 0.0292 r 4 n 4 1 4 = 4000(1.0073) nt A = P 1 + EXAMPLE 5 Find the balance in an account SOLUTION a.With interest compounded quarterly, the balance after 1 year is: Write compound interest formula. P = 4000, r = 0.0292, n = 4, t = 1 Simplify. Use a calculator. = 4118.09 ANSWER The balance at the end of 1 year is $4118.09.

  18. 365 1 = 4000 1 + r 0.0292 365 n 365 = 4000(1.00008) ANSWER nt A = P 1 + The balance at the end of 1 year is $4118.52. EXAMPLE 5 Find the balance in an account b. With interest compounded daily, the balance after 1 year is: Write compound interest formula. P = 4000, r = 0.0292, n = 365, t = 1 Simplify. Use a calculator. = 4118.52

  19. ANSWER $2254.98 r 0.04 n 365 1095 = 2000(1.00011) nt A = P 1 + for Example 5 GUIDED PRACTICE 6. FINANCE You deposit $2000 in an account that pays 4% annual interest. Find the balance after 3 years if the interest is compounded daily. a.With interest compounded daily, the balance after 3 years is: Write compound interest formula. 3 365 P = 2000, r = 0.04, n = 365, t = 3 = 2000 1 + Simplify. = 2254.98 Use a calculator.

  20. 1. Graphy = 2x. State the domain and range. ANSWER 3 2 domain: all real numbers range:y > 0 Daily Homework Quiz

  21. ANSWER 2. Graphy = 3 2x–2– 1. State the domain and range. domain: all real numbers range:y > – 1 Daily Homework Quiz

  22. ANSWER $ 1545.68 Daily Homework Quiz 3. You deposit $1500 in an account that pay 3% annual interest compounded daily. What is the balance in your account after 1 year?

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