Exam 4: Exponential Functions, Logarithms, and E

About how many years does it take for money to double when compounded continuously at 4% per year?

Suppose that t is a small positive number. Estimate the slope of the line containing the points And

Suppose x is such that . Evaluate .

Evaluate assuming that log₇x = 3.7 and log₇y = 4.1.

Suppose a bank wants to advertise that $2,000 deposited in its savings account will double in four years. This bank compounds interest 360 times per year. What annual interest rate must the bank pay?

A human bone is founded in your backyard. The ratio of carbon-14 to carbon-12 in the bone is 40% at the corresponding ratio for living organisms. Calculate the age of the bone.

Find a number t such that ln(3t - 4) = 3.

Estimate the value of Round your answer to the nearest thousandth.

Find a number t such that .

For x = 4.4 and y = 4.9, evaluate each of the following. Round your answer to four decimal places. a) log(xy) b) (log x)(log y)

Suppose a savings account pays 8% interest per year, compounded 6 times per year. If the savings accounts starts with $1,300, how long would it take for the savings account to exceed $6,800?

Suppose that a bank account that compounds interest continuously grows from $1000 to $1100 in 5 years. What annual interest rate is the bank paying? Round your answer to one decimal place.

Find the smallest integer k such that .

Suppose f if a function such that f(1) = 4 and f(4) = 12. Evaluate f(16). Round to 3 decimal places if necessary.

Suppose that a bank account paying 3% interest per year, compounded 3 times per year, contains $44,900 at the end of 15 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Find a number b such that the indicated equality holds.

Suppose a country's population increases by a total of 5% over a 2-year period. What is the continuous growth rate for this country? Round your answer to the nearest hundredth.