1) Solve the following:
Solve the problem.
2) How long will it take an investment to double if it is invested at 7.8%, compounded continuously?
3) An initial investment of $1000 is appreciated for 2 years in an account that earns 6% interest, compounded semiannually. Find the amount of money in the account at the end of the period.
4) A company begins a radio advertising campaign in Chicago to market a new soft drink. The percentage of the target market that buys a soft drink is estimated by the function where t is the number of days of the campaign. After how long will 75% of the target market have bought the soft drink?
5) A certain radioactive isotope decays at a rate of 0.15% annually. Determine the half-life of this isotope, to the nearest year.
6) The population of a small country increases according to the function where t is measured in years. How many people will the country have after 8 years?
Find the value of the expression.
Express as a single logarithm and, if possible, simplify.