MAT 210 Test #1MAT 210 Test #1 1. Let 31)(xxxf(a) [3 pts] Find the domain of f.(b) [3 pts] Find the range of f.(c) [3 pts] Find f(1).(d) [3 pts] Find x if f(x) = 2.2.(a) [4 pts] Let .)( and 13)(2xxgxxf  Find ).1)(( fg (b) [4 pts] Express 24)(xexh  as the composition of two functions, f(x) and g(x), where f(x) x and g(x) x.(c) [4 pts] If xxxf 23)(, find .)()(hxfhxf (d) [4 pts] Write the given quantity in terms log x, log y, and log z:yxzlog(e) [4 pts] Solve for x:log x = 33. The table below lists data relating the number of trees, x, planted in an orchard to the annualMAT 210 Test 1 Page 2revenue, r, in dollars per tree:x 100 104 108 110 112 116 120r 61.50 58.10 55.90 55.20 53.80 52.40 51.10(a) [5 pts] Use linear regression to find the best fitting line that relates the number of trees in theorchard to the annual revenue per tree.(b) [4 pts] Use the model to find the annual revenue per tree when 115 trees are planted in the orchard.(c) [3 pts] Interpret what the slope of the line means. 4. [12 pts] Suppose that 1000 units of a certain item are sold per day by the entire industry at aprice of $85 per unit and that 1250 units can be sold per day by the same industry at a price of $80 per unit. Find the demand equation for p, assuming the demand curve to be a straight line.5. The revenue and cost functions are given by R(x) =xx 205.02and C(x) = 10x + 18 respectively.(a) [4 pts] Find the profit function.(b) [4 pts] Find the break-even quantities.(c) [4 pts] Find the value of x that maximizes profit.6.(a) [6 pts] Suppose $4500 was invested January 1, 1990, in an account which earns 5% compounded continuously. How much will be in the account on January 1, 2010 (assuming no deposits or withdrawals are made)?(b) [6 pts] An account has an annual yield of 10% compounded quarterly. How long will it take for $1000 to double?7.F00A Copyright 2000 Department of Mathematics, Arizona State UniversityMAT 210 Test 1 Page 3(a) [6 pts] Solve for x: 8.7)034.3(2.4 x(b) The following data gives the price of a math book in terms of the year (0 corresponding to 1970.)Year 0 2 4 6 8 10Price $48.95 $53.15 $57.35 $61.55 $65.75 $69.95I. [4 pts] Based on this data, find the best fitting exponential function using exponential regression.II. [5 pts] Using the model obtained in part (a), estimate the price of the book in 1985.III. [5 pts] Using the model obtained in part(a), estimate when the price will reach $90.F00A Copyright 2000 Department of Mathematics, Arizona State