Exponential Logarithmic Graphs Worksheets Grade 11

1. log₂(64) + ln(e⁵) = ?
2. On a coordinate plane, the graph of the function f(x) = 2^x is shown. This exponential curve passes through point A at (3, 8). The graph is then reflected across the line y = x to create the inverse function g(x). What is the y-coordinate of the point on g(x) that corresponds to x = 8?
3. Graph f(x) = 5^(x+2) - 3. Identify the horizontal asymptote and the y-intercept.

…and 5 more problems

1. Matiu is an environmental scientist studying the decline of a native bird population on an island. The population, P(t), after t years is modeled by the function P(t) = 1200 \times (0.85)^t, where t is time in years. Matiu needs to report the year when the population will first fall below 300 birds. Determine the number of years required for the population to reach exactly 300 birds, expressing your answer as an exact value involving logarithms.
2. Graph f(x) = 12^x and g(x) = log₁₂(x) on the same coordinate plane. Identify the asymptote of each function and state the domain and range of both.
3. log₂(64) - ln(e⁴) = ?

…and 4 more problems

1. Matiu is a financial analyst modeling the growth of an investment fund. The fund's value V(t) in thousands of dollars after t years is given by the function V(t) = 12 × 3^(t/5). Hana, his colleague, is tracking a different fund that decreases in value according to W(t) = 50 × (1/2)^(t/4). Matiu wants to know the time when the value of his fund will be exactly 4 times the value of Hana's fund. Determine the value of t that satisfies V(t) = 4 × W(t). Express your answer as an exact value using logarithms.
2. Matiu is an environmental scientist studying the pH levels of a lake affected by acid rain. He models the hydrogen ion concentration (in moles per liter) over time using the function H(t) = 3.16 × 10^(-5) × 2^(t/4), where t is the number of weeks after the initial measurement. The pH of a solution is defined as pH = -log₁₀(H), where H is the hydrogen ion concentration. Matiu knows that a pH below 5.0 is harmful to aquatic life. By graphing the pH as a function of time, determine the number of weeks it will take for the lake to reach a harmful pH level of exactly 5.0. Express your answer as an exact value involving logarithms.
3. Charlotte is analyzing the cooling of a ceramic piece in a kiln. The temperature T(t) in degrees Celsius of the ceramic after t minutes is modeled by the function T(t) = 27 + 72(2)^(-t/7). Identify the horizontal asymptote of this function and explain its meaning in the context of the ceramic's cooling process. Then, determine the time, to the nearest tenth of a minute, when the ceramic's temperature reaches 51 degrees Celsius.

…and 3 more problems