# MAT 117/117S Problem Set 4

MAT 117/117S Problem Set 4 (5 points for each question) 1. Find the difference quotient 𝑓(𝑥+ℎ)−𝑓(𝑥) ℎ , where h ≠ 0, for the function below. f(x) = 4𝑥 2 − 3 Simplify your answer as much as possible. 2. A species of animal is discovered on an island. Suppose that the population size P(t) of the species can be modeled by the following function, where time t is measured in years. P(t) = 320 1+4𝑒 −0.46𝑡 Find the initial population size of the species and the population size after 8 years. Round your answers to the nearest whole number as necessary. Initial population size: ___________________ individuals Population size after 8 years: ______________ individuals 3. Solve for x in the equation 𝑒 8𝑥 = 4 Round your answer to the nearest hundredth. Do not round any intermediate computations. 4. Use the properties of logarithms to expand the following expression. log⁡(⁡ 𝑥3 5 𝑧 √𝑦 2 ⁡) Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive. 5. Write the expression as a single logarithm 2 1 4𝑙𝑜𝑔𝑚 𝑤 − 𝑙𝑜𝑔𝑚 𝑧 + 𝑙𝑜𝑔𝑚 𝑦 3 5
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