22. See Problem 3.

    Baking A cake recipe says to bake the cake until the center is 180°F, then let the cake cool to 120°F.

    1. Given a room temperature of 70°F, what is an exponential model for this data set?
    2. How long does it take the cake to cool to the desired temperature?

See Problem 4.

Graphing Calculator Use the graph of y = e x y equals , e to the x  to evaluate each expression to four decimal places.

23. e 6 e to the sixth
24. e − 2 e super negative 2 end super
25. e 0 e to the
26. e 5 2 e super 5 halves end super
27. e e e to the e

See Problem 5.

Find the amount in a continuously compounded account for the given conditions.

28. principal: $2000

    annual interest rate: 5.1%

    time: 3 years

29. principal: $400

    annual interest rate: 7.6%

    time: 1.5 years

30. principal: $950

    annual interest rate: 6.5%

    time: 10 years

B Apply

31. Think About a Plan A student wants to save $8000 for college in five years. How much should be put into an account that pays 5.2% annual interest compounded continuously?
    • What formula should you use?
    • What information do you know?
    • What do you need to find?
32. Investment How long would it take to double your principal in an account that pays 6.5% annual interest compounded continuously?
33. Error Analysis A student says that the graph of f ( x ) = ( 1 3 ) x + 2 + 1 f open x close equals . open , 1 third , close super x plus 2 end super . plus 1  is a shift of the parent function 2 units up and 1 unit to the left. Describe and correct the student's error.
34. Assume that a is positive and b ≥ 1 . b greater than or equal to 1 .  Describe the effects of c > 0 , c greater than 0 comma   c = 0 , c equals 0 comma  and c < 0 c less than 0  on the graph of the function y = a b c x . y equals . eh b super c x end super . .

35. 35. Graphing Calculator Using a graphing calculator, graph each of the functions below on the same coordinate grid. What do you notice? Explain why the definition of exponential functions has the constraint that b ≠ 1 . b not equal to 1 .

    y = ( 1 2 ) x y equals . open , 1 half , close to the x

    y = ( 8 10 ) x y equals . open , 8 tenths , close to the x

    y = ( 9 10 ) x y equals . open , 9 tenths , close to the x

    y = ( 99 100 ) x y equals . open , 99 over 100 , close to the x

36. Botany The half-life of a radioactive substance is the time it takes for half of the material to decay. Phosphorus-32 is used to study a plant's use of fertilizer. It has a half-life of 14.3 days. Write the exponential decay function for a 50-mg sample. Find the amount of phosphorus-32 remaining after 84 days.
37. Archaeology Archaeologists use carbon-14, which has a half-life of 5730 years, to determine the age of artifacts in carbon dating. Write the exponential decay function for a 24-mg sample. How much carbon-14 remains after 30 millennia? (Hint: 1 millennium = 1000 years)

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