MAT 117/117S Problem Set 4

MAT 117/117S Problem Set 4 (5 points for each question) 1. Find the difference quotient 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯) β„Ž , where h β‰  0, for the function below. f(x) = 4π‘₯ 2 βˆ’ 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 βˆ’0.46𝑑 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 8π‘₯ = 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⁑(⁑ π‘₯3 5 𝑧 βˆšπ‘¦ 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 4π‘™π‘œπ‘”π‘š 𝑀 βˆ’ π‘™π‘œπ‘”π‘š 𝑧 + π‘™π‘œπ‘”π‘š 𝑦 3 5
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