GMAT Exponents Practice Questions

A hospital administers a drug whose concentration in a patient's bloodstream decays exponentially according to the function $C(t) = C_0 \cdot 2^{-kt}$, where $t$ is in hours. If the drug's half-life is 3 hours, what fraction of the initial concentration $C_0$ remains after 9 hours?

A boutique first increased the price of a designer jacket by 50%, then reduced the new price by 1/3. The final price can be expressed as the original price multiplied by what exponent of 2?

A laboratory measures that a radioactive sample decays to 12.5% of its original mass after a certain time period. If the decay follows the equation $M = M_0 \times 2^{-t/h}$, where $h$ is the half-life in hours, how many half-lives $t/h$ have passed when the mass reaches 12.5% of $M_0$?

At a carrot packing shed, water from the first rinse is filtered and sent back for another rinse. Each completed pass leaves 1/4 of the fine silt that was present at the start of that pass, and after a shift on one line the silt is 1/64 of the amount before the shift. Pump A can complete one pass in 4 hours and runs for all 8 hours of the shift. Pump B can complete one pass in 6 hours and runs only the first 6 hours before it is switched off. The pumps work independently at constant rates, and their completed passes add. For the five rinse lines, the numbers of completed passes are nonnegative integers with median 2, mode 3, and range 3, where range means greatest minus least. The studied line completed more passes than the median and fewer than 4; both comparisons are strict. The number of passes completed on the studied line is what percent of the number of passes Pump A alone would complete in 8 hours?

A hotel's standard room rate changes by a factor of $\sqrt[3]{1.728}$ one month, then changes by a factor of $\sqrt{0.64}$ the following month. The final rate is what multiple of the original rate?

A community garden coordinator surveyed 60 member households that grow blueberry bushes. Every household answered two yes or no questions: Did you add fresh mulch this spring, and did you later check the mulch depth around your bushes. Each household is in exactly one of the four yes or no combinations, the two answers are not assumed to be independent, and all counts are whole numbers. Exactly 75% of the households added fresh mulch, and exactly 2/3 of the households checked the depth. Of the households that checked the depth, 5 had not added fresh mulch. For households that added mulch and checked the depth, the depth was 4 inches right after adding and 9/4 inches two months later. For households that added mulch but did not check the depth, the depth was 5 inches right after adding and 16/5 inches two months later. In each of these two groups the depth decreased by the same percent in each of the two months, with exactly two monthly decreases and with the starting measurement not counted as a decrease. Each household that added fresh mulch has 2 blueberry bushes, and 1 cubic foot of mulch raises the depth around one bush by 1/6 inch. Using the household counts as weights, how many cubic feet of mulch are needed to raise the average depth around all bushes in households that added fresh mulch from its one month level to 4 inches?

On two mornings, a person spends a different, nonnegative whole number of minutes choosing an outfit. The two times total 44 minutes. For a morning when the selection takes t minutes, the stress index is 2 raised to the power |√$t + 7$ - 5|. Given that the stress indices on the two mornings are equal, what is the shorter selection time?

A blockbuster film's daily box office revenue follows an exponential decay model after its opening weekend. The revenue (in millions of dollars) on day t is given by $R(t) = 120 \times (0.85)^{t - 1}$, where day 1 is the first day after opening weekend. The studio considers the theatrical run complete when daily revenue falls below $20 million. What is the first integer day t when this condition is met?

A recycling plant processes materials in batches where each batch's capacity is measured in power-of-2 units. The current batch uses a combination of two processes: the first uses 32 units and the second uses 64 units. The plant manager wants to express the total capacity as a single power of 2. What is the total capacity expressed as a power of 2?