1. Your savings account grows by continuous compounding of interest. The yearly percentage growth rate for the account balance M (in dollars) is 4.5%, and your initial investment is $250.
(a) Find a formula for M as a function of the time t in years since you opened the account.
(b) What is the monthly percentage growth rate for this account?
2. You deposit some money in a savings account and let the deposited money collect interest. The following table shows your balance B (in dollars) as a function of time t, measured in years since your initial deposit.
t 0 1 2 3
B 125.00 130.75 136.76 143.06
(a) By calculating ratios, show that the data is exponential. (Round the ratios to 3 decimal places.)
(b) Find a formula for the exponential function giving the balance B as a function of timet.
(c) What is the yearly percentage growth rate for this account?
(d) What is the decade percentage growth rate for this account?
(e) Use a table of values on the calculator to estimate how long it will take for your initial investment to double in size.
3. You are saving money with the hope of buying a new car after several years. Both the balance in your savings account and the cost of the car grow exponentially over time. Let tbe time in years since the start of 1998.
(a) The cost C (in dollars) of the car at the start of 1998 is $14,000, and the yearly growth factor for the cost is 1.02. Find a formula for C as a function of t.
(b) At the start of 1998 you invest $12,000 in a savings account. The yearly percentage growth rate for the account balance B (in dollars) is 4.3%.
i. Find the yearly growth factor for B.
ii. Find a formula for B as a function of t.
iii. Use your answer to Part (a) and to Part (ii) above to determine at what time your account balance will be large enough so that you are able to afford the new car.
4. An earthquake in California measured 3.4 on the Richter scale.
(a) An earthquake in Oklahoma measured 1.2 on the Richter scale. How did the power of the Oklahoma quake compare with that of the California quake?
(b) An earthquake in Chile was 3 times as powerful as the California quake. What Richter scale reading did the Chilean earthquake have?
5. Recall that pH is a measure of the acidity of a solution and that lower pH values indicate a more acidic solution. If H is the concentration of hydrogen ions in the solution (measured in moles per meter of solution), then pH = -logH.
(a) Solution 1 has a pH of 3. Solution 2 is twice as acidic as solution 1 (meaning that the concentration of hydrogen ions in solution 2 is twice that of solution 1). What is the pH of solution 2?
(b) Solution 3 has a pH of 7. How do the concentrations of hydrogen ions for solutions 1 and 3 compare?
6. Recall that decibels= 10 log(relative intensity).
(a) Sound 1 has a decibel level of 40. Sound 2 has twice the relative intensity of sound
1. What decibel level does sound 2 have?
(b) Sound 3 has a decibel level of 60. How do the relative intensities of sound 1 and sound 3 compare?
7. Suppose logK= 4.1.
(a) What is the value of log(3K)?
(b) If log L = 7, how do K and L compare?
(c) Find the value of K.