Exam 4: Exponential and Logarithmic Functions

Solve the problem. -Ultraviolet solar radiation (UV) is strongly absorbed by ocean water. The intensity of the UV at a particular depth can be calculated using the equation where d is the depth in centimeters is the Intensity at the surface, and I is the intensity at depth d. Find the depth at which the intensity is 20% of its value At the surface. Round to the nearest tenth when necessary.

Write the equation of the graph in its final position. -The graph of y = ln(x) is translated 2 units to the right, reflected in the x-axis, and then translated 7 units downward.

Use a graph or a table to find the limit. -

Graph the function. -

Solve the problem. -If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 5.5%? Round to the nearest tenth.

Simplify the expression. -

Use a calculator and the base-change formula to find the logarithm to four decimal places. -

Solve the problem. -At what interest rate must $4700 be compounded annually to equal $12,119.11 after 14 yr? (Round to the nearest percent.)

Find the value of the logarithmic function. -

Rewrite the expression as a single logarithm. -

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation. -

Solve the problem. -Coffee is best enjoyed at a temperature of 115°F. A restaurant owner wants to discover the temperature T at which he should serve his coffee so that it will have cooled to this ideal temperature in 6 minutes. He discovers That a cup of coffee served at 197°F cools to 185°F in one minute when his restaurant is at 75°F. If he maintains The restaurant temperature at 75°F, at what temperature should he serve the coffee to meet his goal?

Solve the equation. -

Solve the equation. -

Write the equation of the graph in its final position. -The graph of y = is translated 9 units to the right, reflected in the y-axis, and then translated 4 units downward.

Rewrite the expression as a sum or difference of logarithms or multiples of logarithms. -

Rewrite the expression in terms of log(2) and log(5). -

Use a graphing calculator to solve the equation. Round to two decimal places. -

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $12,000 is appreciated for 5 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Solve the problem. -A certain noise produces of power, designated as S. What is the decibel level of this noise? Round to the nearest decibel.)