Hello, I need help with these grade 12 university level calculus and vector math questions, please. For a good review please be detailed and thorough when answering the questions. And please answer all the questions correctly too :) Thank you !

Application of Exponential, Logarithmic and Trigonometric Functions 1. A biologist is studying the increase in the population of a particular insect in a provincial park. The population triples every week. Assume the population continues to increase at this rate. Initially, there are 100 insects. The population of the insect can be modeled by the equation N(t) = (100)3t Where t represents the time in weeks. a) Determine the number of insects present after 4 weeks. b) How fast is the number of insects increasing when they are initially discovered? c) How fast is the number of insects increasing at the end of 4 weeks? 2. Laura has just bought a new motorcycle for $10,000. The value of the motorcycle depreciates over time. The value can be modelled by the function t V(t) = 10 0006T (this is an e raised to the exponent (E) in case it wasn't clear. a) At what rate is the value of the motorcycle depreciating the instant Laura drives it off the dealer's lot? b) Laura decides that she will stop insurance coverage for collision once the motorcycle has depreciated to one quarter of its initial value. When should Laura stop her collision coverage? c) At what rate is the motorcycle depreciating at the time determined in part b)? 3. The position of an object is given by 3(t) = 2 + 7cos (t) Determine all the points where the object is not moving where 0 S t S 41:. 4. A particle is moving along the x-axis according to 5(t) : t + sin (I?) where t is in seconds, it 2 0, and 3(t) is in meters. a) Give the velocity function of the particle in terms of t. b) How fast is the particle traveling at TE seconds? c) What is the average velocity in the first 21: seconds? d) When is the particle at rest