1) The Exponential Growth: A bacterial culture starts with 500 bacteria and doubles every hour. How many bacteria are there after 3 hours? a) 1000 b) 2000 c) 4000 d) 8000 2) The Quadratic Equation: A ball is thrown upward with an initial velocity of 64 ft/s from a height of 80 ft. Its height (h) after t seconds is given by the equation h(t) = -16t2 + 64t + 80. At what time (t) does the ball reach its maximum height? a) 1 second b) 2 seconds c) 3 seconds d) 4 seconds 3) The Trigonometric Function: A Ferris wheel with a radius of 50 feet rotates at a constant speed, completing one revolution every 20 seconds. What is the height of a rider above the ground after 5 seconds, if the rider starts at a bottom of the wheel? (Assume the bottom of the wheel is at ground level.) a) 25 feet b) 50 feet c) 75 feet d) 100 feet 4) The Logarithmic Equation: The magnitude of an earthquake is measured using the Richter scale, given by M = log10(l/l0), where l is the intensity of the earthquake and l0 is a reference intensity. If an earthquake has an intensity 10,000 times greater than the reference intensity, what is its magnitude on the Richter scale? a) 2 b) 3 c) 4 d) 5 5) The Calculus Problem: Find the derivative of the function f(x) = 3x2 - 6x + 2 a) 6x - 6 b) 3x2 - 6 c) 6x + 2 d) 3x - 6

Advanced Math Challenge: Word Problem

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