Exponential Logarithmic Graphs Worksheets Grade 11

1. Olivia is investigating the spread of a rare plant species in a protected wetland. The area covered by the plant, in square meters, is modeled by the function A(t) = 7 × 3^(t/5), where t is the number of years since the study began. Emma, her colleague, is studying a different plant species whose area is modeled by B(t) = 21 × 3^(t/5). Emma claims that her graph is a vertical shift of Olivia's graph. Is Emma correct? If not, describe the correct transformation from A(t) to B(t), identify the horizontal asymptote of each function, and state the y-intercept of A(t).
2. Graph f(x) = 3^(x+1) - 2 and identify the horizontal asymptote.
3. A radioactive substance decays according to the function N(t) = 100e^(-0.0231t), where N is the amount remaining in grams and t is time in years. The graph of this function shows exponential decay. After how many years will exactly half of the original 100 grams remain?

…and 4 more problems

1. Graph f(x) = 6^x and g(x) = log_6(x) on the same coordinate plane. Identify the asymptote of f(x) and the domain of g(x).
2. Aroha is a geochemist studying the groundwater contamination at a former industrial site. The concentration of a pollutant, in parts per billion (ppb), decreases exponentially over time according to the function C(t) = 1500 * (0.92)^t, where t is the number of years since the contamination source was removed. Aroha needs to determine when the concentration will drop to 30 ppb, the safe drinking water standard. Write an equation that models this situation and solve for the number of years required, expressing your answer in terms of logarithms.
3. Mason is a computer scientist modeling the performance of a new cooling system for a high-performance processor. The temperature T (in degrees Celsius) of the processor after t minutes is modeled by the function T(t) = 27 + 72e^(-0.12t). Sketch the graph of this function, labeling the horizontal asymptote and the y-intercept. What is the long-term temperature of the processor as t approaches infinity?

…and 4 more problems

1. A radioactive substance decays according to the function N(t) = 100e^(-0.0231t), where N is the mass in grams and t is time in years. On a coordinate plane, the exponential decay curve passes through point P, which has coordinates (30, y). What is the y-coordinate of point P, representing the remaining mass after 30 years?
2. log₂(64) - ln(e⁴) = ?
3. A city's population is currently 250,000 people and is growing at an annual rate of 4.2%. Urban planners need to determine when the population will reach 400,000 people. Write an equation that models this situation and solve for the number of years required, expressing your answer in terms of logarithms.

…and 4 more problems