Logarithms Solve Exponential Worksheets Grade 11

1. Aroha is a conservation biologist studying the recovery of a native bird population on a predator-free island. The number of birds, N(t), after t years is modeled by the function N(t) = 7 × 5^(0.3t). The island's ecosystem can sustainably support a maximum of 875 birds. How many years will it take for the bird population to reach this sustainable capacity? Use logarithms to solve.
2. 4^(2x) = 48
3. Mere is analyzing the growth of a bacterial colony on a Petri dish. The colony grows exponentially according to the equation A = 15 * 4^(t), where A is the area of the colony in square millimeters after t hours. On a graph of this exponential growth, the point where the colony reaches an area of 240 square millimeters is marked. Using logarithms, determine the value of t when A = 240.

…and 4 more problems

1. 4^(2x - 1) = 60
2. A sound wave's intensity I is measured in decibels using the formula β = 10 log(I/I₀), where I₀ = 10⁻¹² W/m² is the reference intensity. If a rock concert measures 115 decibels, what is the intensity I of the sound wave in W/m²?
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (5,0), and (0,12). The hypotenuse extends from (5,0) to (0,12). A student draws a circle that circumscribes this triangle, passing through all three vertices. What is the area of this circumscribed circle?

…and 5 more problems

1. Dr. Chen is studying bacterial growth in a lab culture. The number of bacteria doubles every 4 hours. If she starts with 500 bacteria, how many hours will it take for the population to reach 32,000 bacteria? Use logarithms to solve.
2. 14^(x - 5) = 89
3. 5^(2x - 1) = 125^x

…and 5 more problems