# Use exponential and logarithmic equations in

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Use Exponential and Logarithmic Equations in Applications19. If \$20,000 is invested in an account earning 2.5% interest compounded continuously, determine how long it will take the money to grow to \$45,000. Round to the nearest year. Use the model rtAPe20. The following formula relates the energy E (in joules) released by an earthquake of magnitude M.. 14
log5.241.44EM(M> 5)What is the energy released by a magnitude 6 and a magnitude 7 earthquake?
Section 4.6Modeling with Exponential and Logarithmic Functions15
Exponential growth function:A tA ekt( )Where A= Amount present after time “t; A= Initial quantity presentk = Growth constant,This is an increasing function as e > 1, and k > 0.A tA ekt( )is a decreasing function, known as Exponential decay function.Half-life: If a quantity decays exponentially, the amount of time that it takes to become one-half its original amount is called the half - life. 1.Suppose that at 19 years old you win \$100,000 playing the lottery. If you would like to have \$1,000,000 when you retire at age 67, determine the average rate of return needed undercontinuous compounding. 2.A sample collected from cave paintings on an archeological site in France shows that only 2% of the carbon-14 remains. How old is the sample? Round to the nearest year.Use the model for radiocarbon dating:0.0001210tQ tQ ewhere 0is the original quantity of carbon-14.3.The size P of a certain insect population at time t days obeys the function:0.02 t= 500 eP ta.Determine the number of insects at t = 0 days.b.What is the growth rate of the insect population?c.Graph the function on your calculator.d.What is the population after 10 days?e.When will the population reach 800?f.When will the population double?4.Strontium – 90 is a radioactive material that decays according to the function: - 0.0244 t0= AeA tWhere t is in years. Assume that a scientist has a sample of 500 grams of strontium – 90.a.What is the decay rate of strontium – 90?a.Graph the function on your calculator.b.How much strontium is left after 10 years?c.When will 400 grams of strontium – 90 be left?d.What is the half – life of strontium – 90?Q. Newton’s Law of Cooling:16