Exam 4: Logarithmic Functions and Exponential Modela

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 5 days for several months. As of July 27, 2009, the number of new cases was 26116. Which one of the following exponential functions model the growth of this virus?

If , then . Assume that is a one-to-one function.

The half-life of Radon-222 is 3.8 days. A 32-gram sample of Radon-222 is monitored for one day. How long will it take for the sample to be 24% of the initial amount? (rounded to the nearest hundredths)?

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 5 days for several months. As of July 27, 2009, the number of new cases was 17,871. Determine the instantaneous growth rate for the virus (rounded to the nearest ten-thousandths).

Solve the logarithmic equation for . Round to the nearest hundredth.

For any , the logarithm function is always decreasing.

Which of the following is the correct missing value in the table for the function ?

Which one of the following exponential equations is equivalent to .

On August 18, 2009, a 6.3 magnitude earthquake was detected south of the Fiji Islands. On August 23, 2009, a 5.2 magnitude earthquake was detected in the same area. How many times more intense was the August 18th earthquake than the August 23rd earthquake? (Rounded to the nearest hundredth)

Find the logarithm of .

Solve the exponential equation for . Round to the nearest thousandth.

The number of bees in a certain area of Arizona is modeled by the function where is measured in number of weeks. Determine the number of bees after 17 weeks. Rounded to the nearest whole number.

Which one of the following graphs represents the function ?

A car dealer advertises a 35% discount on all cars available in the current inventory. In addition, the car dealer offers a $1800 rebate on the purchase of a new care. The dealer decides to apply the rebate first and then award the 35% discount afterwards. Let represent the sticker price of the new car. Which one of the following functions model the final price of the car once the rebate and discount have been awarded?

Solve the exponential equation for . Round to the nearest thousandth.

Solve the exponential equation for . Round to the nearest thousandth.

The mass of bacteria in a Petri dish is 30 micrograms. After 3 hours, the bacteria s mass as increased to 141 micrograms. Which one of the following exponential functions model the bacteria s growth, where is measured in hours.

Find the inverse of .

If the hydrogen ion concentration of a soil sample is , what is the pH level of the soil?

For the exponential model , what is the instantaneous growth or decay rate.