The population of a dying town is modelled by P(t) = Poet the k an unknown constant (or P(t) = P₁ · bt with b and unknown constant. The initial population of the town is 604. at t = 5 years after the initial measurement, the population is 404. What will the population bet = 15 years after the initial measurement? Your answer should be rounded to the nearest whole number. Remark: When you find the constant k or b, if you do not record this constant within a fairly high precision, your resulting answer will not be accutate within the nearest whole number.

The number of streetlights in a town is growing linearly. Four months ago (t = 0) there were 47 lights. Now (t = 4) there are 107 lights. If this trend continues, (a) Find an explicit formula for the number of lights in month t. P₁ = lights (b) How many months will it take to reach 211 lights? Round your answer to the nearest month. months.

After taking a certain antibiotic, the amount of amoxicillin A(), in milligrams, remaining in the patient's system t hr after taking 1,000 mg of amoxicillin is A(t) = 1,000e-0.49t How much amoxicillin is in the patient's system 3 hr after taking the medication? Round to the nearest tenth of a mg.

B C D At a concert, a band is playing on a platform that extends P feet from a wall behind the band, and the platform is rising from ground level, as shown in the figure above. A light source is L feet from the wall, and the platform casts a lengthening shadow on the wall as the platform rises. At time t seconds, the platform is h feet above the ground, and the height of the shadow is s feet. The quantities are related by the equation (h+s) = 8, where L and Pare constants. Which of the following best expresses the rate of change of h with respect to time in terms of the rate of change of s with respect to time? dh dt s ft dh = 1 d h ft =8 S 18-d L ds P dt 8 -P ft- ds dt. L ft