Concept explainers
In Exercises 21–25, solving the
Growth of a Savings Account A person deposits an inheritance of
a. Assume that the withdrawals are made at a continuous rate. Set up a differential equation that is satisfied by the amount
b. Determine
c. With the help of your calculator, plot
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CALCULUS+ITS APPLICATIONS
- he table shows the total assets (in trillions) held in a foreign bank for the given years. Complete parts (a) through (c) below. Year 2000 | 2005 | 2007 | 2009 | 2011 | 2013 | 2015 Assets 16 40 54 80 117 152 200 (a) Find an exponential model of the form f(t) =yob' for these data, where t= 0 corresponds to the year 2000. If you do not have suitable technology, use the first and last data points to find a function. If you have a graphing calculator or other suitable technology, use exponential regression to find a function. The exponential model for the data is f(t) =WD. (Round to three decimal places as needed.)arrow_forward2 Find a formula for the exponential function passing through the points (-1,) and 5 (1,10) y = 0 acerarrow_forward2. Many countries have a population growth rate of 3% (or more) per year. At this rate, how many years will it take a population to double? Use the model A = Aoert.arrow_forward
- 8) Determine the equation of an exponential function of the form y = a · b* that contains the points (4,-486) and (5, -1458).arrow_forwardModel the following data using an exponential function of the form f(x) = Ab". You need to do this rigorously, that is, set up a system of equations, and solve it to get A and b. Getting the right answer by guessing will earn no credit. (a) f(x) is exponential and goes through the points (1, 2) and (4,6). (b) f(x) is exponential and goes through the points (2, 75) and (5, 9375).arrow_forward3. Find the formula for the exponential function passing through the points (0,1.5) and (1,5).arrow_forward
- Exer. 31-32: Find an exponential function of the form f(x) = ba-* + c that has the given horizontal asymptote and y-intercept and passes through point P. 31 y = 32; y-intercept 212; P(2, 112) 32 y = 72; y-intercept 425; P(1, 248.5)arrow_forwardproblen 1.1arrow_forwardThe table shows the total assets (in trillions) held in a foreign bank for the given years. Complete parts (a) through (c) below. 2000 | 2005 | 2007 | 2009 | 2011 | 2013 | 2015 78 Year Assets 17 42 52 117 150 199 (a) Find an exponential model of the form f(t) = y,b' for these data, where t= 0 corresponds to the year 2000. If you do not have suitable technology, use the first and last data points to find a function. If you have a graphing calculator or other suitable technology, use exponential regression to find a function. The exponential model for the data is f(t) =I0' (Round to three decimal places as needed.)arrow_forward
- The amount of money A in an account with an Interest rate r compounded annually Is glven by A=P(1+r)' where P is the initlal principal and t is the number of years the money Is Invested. Part 1 of 3 (a) If a $10,000 investment grows to $11,236 after 2 yr, find the interest rate. The interest rate is Part 2 of 3 (b) If a $7000 investment grows to $8316.70 after 2 yr, find the Interest rate. The interest rate is %. Save For Later Check 2021 McGraw-Hill Education AlL Rights Resenved Terms of Usearrow_forward(2) The annual net profit for a company, from 1995 to 2005, can be approximated by the model an 10e0.2n, n = 1, 2, 3, ., N, where an is the annual net profit in millions of dollars, and n represents the year, with n =1 corresponding to 1995. Estimate the total net profit during this period. (3) A deposit of 15 dollars is made at the beginning of each month, for a period of 5 years, in an account that pays 0.9 % interest, compounded monthly. Find the balance in the account at the end of the 5 years. (4) A deposit of 20 dollars is made every 3 months, for a period of 10 years, in an account that pays 1% interest, compounded quarterly. Find the balance in the account at the end of the 10 years. (5) A deposit of $500 can be made with two options: earn 2% interest, compounded quarterly for 3 years, or earn 1.5%, compounded monthly for 3 years. Find the balance after 3 years of both options.arrow_forwardSolve 2(a) for at least iii or i.These question focus on exponential growth and decay.arrow_forward
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