Exponential Functions and Real Life Problems：指数函数与现实生活中的问题.docVIP

Exponential Functions and Real Life Problems: Any positive number can be used as the base for an exponential function, but some bases are used more frequently than others. Bases 2 and 10 are one of the more frequently used ones. The most important base is the number denoted by the letter . The number is defined as the value that approaches as becomes large. 1 2.00000 5 2.48832 10 2.59374 100 2.70481 1,000 2.71692 10,000 2.71815 100,000 2.71827 1,000,000 2.71828 From the table we can see that, correct to five decimal places. In fact the value of to 20 decimal places is (The notation was chosen by Leonhard Euler, probably because it is the first letter in the word exponential) The natural Exponential Function: is the exponential function with base . It is often referred to as the exponential function. Evaluate each expression correct to five decimal places: 1) 2) 3) 4) An infectious disease begins to spread in a small city of population 10,000. After days, the number of persons who have succumbed to the virus is modeled by the function: How many infected people are there initially, after one day, two days and five days? Compound Interest: is calculated by the formula Where: amount after years principal interest rate per year number of times interest is compounded per year number of years 5) A sum of $2000 is invested at an interest rate of 7% per year. Find the amounts in the account after 10 years if interest is compounded annually, semiannually, quarterly, monthly, and daily. 6) A sum of $1000 is invested at an interest rate of 12% per year. Find the amounts in the account after 3 years if interest is compounded annually, semiannually, quarterly, monthly and daily. Continuously Compounded Interest: is calculated by the formula Where amount after years principal interest rate per year number of years 7) Find the amount after 4 years if $1100 is invested at an interest rate of 11% per yea