Calculus 1.7

6^=9

1.226

Find the future value in 13 years of a $15,000 payment today, if the interest rate is 2.6% per year compounded continuously.

21032.11$

Suppose is invested in an account paying interest at a rate of per year. Round your answers to two decimal places. (a) How much is in the account after years if the interest is compounded annually? 1)The account will contain ????? after years. (b) How much is in the account after years if the interest is compounded continuously? 2)The account will contain ????? after years. Click if you would like to Show Work for this question: Open Show Work

1) 1435.68$ 2)11446.29$

In 1923, koalas were introduced on Kangaroo Island off the coast of Australia. In 1996, the population was 5000. By 2005, the population had grown to 27,000, prompting a debate on how to control their growth and avoid koalas dying of starvation.1 Assuming exponential growth, find the (continuous) rate of growth of the koala population between 1996 and 2005. 1) continuous growth rate? 2)P(t)= 3)The population in the year 2012 will be approximately

1) 18.7% 2)5000e^0.187t 3) 99627 Koalas

The exponential function y(x)=Ceαx satisfies the conditions y(0)=5 and y(1)=9. (a) Find the constants C and α. Enter the exact value of α. Enclose arguments of functions, numerators, and denominators in parentheses. For example, sin(2x) or (a−b)/(1+n). 1)C= 2)a= 3)y(2)=

1)5 2)ln(9/5) 3)81/5

Whooping cough was thought to have been almost wiped out by vaccinations. It is now known that the vaccination wears off, leading to an increase1 in the number of cases, w, from 1248 in 1981 to 25,827 in 2004. (a) With t in years since 1980, find an exponential function that fits this data. Round numbers to three decimal places if necessary. The number of cases is w= . (b) What does your answer to part (a) give as the average annual percent growth rate of the number of cases? Round your answer to two decimal places. The annual percent growth rate is (c) On May 4, 2005, the Arizona Daily Star newspaper reported (correctly) that the number of cases had more than doubled between 2000 and 2004. Does your model confirm this report? Explain. No. The model predicts that the number of cases increased by about 69% in the period 2000 - 2004. The rate of growth must have been higher from 2000 to 2004 than the average from 1981 to 2004. Yes. The model predicts that the number of cases increased by about 169% in the period 2000 - 2004. The rate of growth must have been lower from 2000 to 2004 than the average from 1981 to 2004. No. The model predicts that the number of cases increased by about 69% in the period 2000 - 2004. The rate of growth must have been lower from 2000 to 2004 than the average from 1981 to 2004. Yes. The model predicts that the number of cases increased by about 169% in the period 2000 - 2004. The rate of growth must have been higher from 2000 to 2004 than the average from 1981 to 2004. Yes. The model predicts that the number of cases increased by about 169% in the period 2000 - 2004. This corresponds to the number of cases more than doubling.

1. 1093.965*1.1408^t 2.14.08 3. No higher

The number of passengers using a railway fell from 191357 to 178899 during a five year period. Find the annual percentage decrease over this period. Round your answer to 1 decimal place.

1.3

Find the present value of a $17,000 payment to be made in 8 years. The interest rate is 3.6% per year compounded continuously.

12745.95$

Find the doubling time of a quantity that is increasing annually by per year. Round your answer to two decimal places. The doubling time is roughly

14.21 years

The company that produces Cliffs Notes (abridged versions of classic literature) was started in 1958 with and sold in 1998 for . Find the annual percent increase in the value of this company over the years. Round your answer to one decimal place. The value of the company increased at an average rate of Enter your answer in accordance to the question statementEntry field with correct answer per year.

22.6 per year

If you need in your bank account in years, how much must be deposited now? The interest rate is , compounded continuously. Round your answer to the nearest dollar. The deposit required is

22973.57$

From October 2002 to October 2006 the number N(t) of Wikipedia articles1 was approximated by N(t)=N0et/500 where t is the number of days after October 1, 2002. The doubling time for the number of Wikipedia articles during this period is:

347 days

In the 1990s, Brazil had a deforestation rate of about 0.48% per year.1 (This is the rate at which land covered by forests is shrinking.) Assuming the rate continues, what percent of the land in Brazil covered by forests in 1990 will be forested in 2035? Give your answer correct to 3 decimal places. % of the land will be covered in forests 45 years later if the rate continues.

80.531

The half-life of radioactive strontium- is years. In 1960, radioactive strontium- was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only of the original amount absorbed remains? Round your answer to the nearest integer. It takes approximately Enter your answer in accordance to the question statement ????? years until only of the original amount absorbed remains. the absolute tolerance is +/-1

82.264 years