433 4.2 Exponential Functions Solve each problem. See Examples 7-9. 97. Future Value Find the future value and interest earned if $8906.54 is invested for 9 yr at 3% compounded (a) semiannually (b) continuously. 98. Future Value Find the future value and interest earned if $56,780 is invested at 2.8% compounded (a) quarterly for 23 quarters (b) continuously for 15 yr. 99. Present Value Find the present value that will grow to $25,000 if interest is 3.2% compounded quarterly for 11 quarters. 100. Present Value Find the present value that will grow to $45,000 if interest is 3.6% compounded monthly for 1 yr. 101. Present Value Find the present value that will grow to $5000 if interest is 3.5% compounded quarterly for 10 yr. 102. Interest Rate Find the required annual interest rate to the nearest tenth of a percent for $65,000 to grow to $65,783.91 if interest is compounded monthly for 6 months. 103. Interest Rate Find the required annual interest rate to the nearest tenth of a percent for $1200 to grow to $1500 if interest is compounded quarterly for 9 yr. 104. Interest Rate Find the required annual interest rate to the nearest tenth of a percent for $5000 to grow to $6200 if interest is compounded quarterly for 8 yr. Solve each problem. See Example 10. 105. Comparing Loans Bank A is lending money at 6.4% interest compounded annu- ally. The rate at Bank B is 6.3% compounded monthly, and the rate at Bank C is 6.35% compounded quarterly. At which bank will we pay the least interest? 106. Future Value Suppose $10,000 is invested at an annual rate of 2.4% for 10 yr. Find the future value if interest is compounded as follows. (a) annually (b) quarterly (c) monthly (d) daily (365 days) (Modeling) Solve each problem. See Example 11. 107. Atmospheric Pressure The atmospheric pressure (in millibars) at a given altitude (in meters) is shown in the table. AMitude Pressure Altitude Pressure 1013 6000 472 1000 899 7000 411 2000 795 8000 357 3000 701 9000 308 ea 4000 617 10,000 ut owon sn 265 LEEVSCA SO00 541 Source: Miller, A. and J. Thompson, Elements of Meteorology, Fourth Edition, Charles E. Merrill Publishing Company, Columbus, Ohio. (a) Use a graphing calculator to make a scatter diagram of the data for atmospheric pressure P at altitude x. (b) Would a linear or an exponential function fit the data better? (c) The following function approximates the data. P(x) = 1013e-0.0001341x Use a graphing calculator to graph P and the data on the same coordinate axes. (d) Use P to predict the pressures at 1500 m and 11,000 m, and compare them to the actual values of 846 millibars and 227 millibars, respectively.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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