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- On the day a grandchild is born, a grandparent deposits $2500 in a fund earning 7.5% interest, compounded continuously. Determine the balance in the account on the grandchild’s 25th birthday.Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?A battery has an expected life (miles) as follows N(300000,10000). If there are 100000 cars in the population of cars sold last year. How many cars would be expected to exceed a battery life of 290000 miles?
- A person has invested some amount in the stock market. At the end of thefirst year the amount has grown by 25 percent profit. At theend of the second year his principal has grown by 40 percent and in the third year, there was a decline of 20%. What is the average rate of increase of his investment during the three years?If : Present Value (PV) of a bond= $8000 Number of Years (N) it takes to mature = 20years. Interest Rate (r) = 7% Using the rule of 70, what is the Future Value (FV) ?A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases expo-nentially with time. At the end of 3 hours there are 10,000 bac-teria. At the end of 5 hours there are 40,000. How many bacteria were present initially?
- The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?A local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it isrepaired the same day. Assume that breakdowns of individual cabs occur completely atrandom at a rate of two per year.c. On the average, how many breakdowns would the fleet expect in a typical threemonth period?A certain forest covers an area of 1900km^2. Suppose that each year this area decrease s by 3%. What will the area be after 11 years?
- (a) find the value of A and a, correct to 3 decimal places,(b) predict the percentage of mathematicians after 15 years, and(c) predict the percentage of mathematicians attending the conference inthe long run.A certain forest covers an area of 2300 km2 . Suppose that each year this area decreases by 3.75% . What will the area be after 5 years?A certain vehicle loses 35% of its value each year if the vehicle has an initial value of $25,000 construct a model that represents the value after T years. Compute the value of the vehicle at the end of the third year. Round to the hundredths place.
