MATH 201 – Brief Calculus Review for Test 31. Find the number of units x that produces a maximum revenue.a) 2500R x x= -b) 2360 4R x x= -2. Find the number of units x that produces minimum average cost per unit. Round to the nearest whole unit. 20.12 15 3000C x x= + +3. Find the price that will maximize profit for the demand and cost function, where p is the price (in dollars), x is the number of units, and C is the cost (in dollars).a) 80p x= - 150 20C x= +b) 50 0.1p x= -35 500C x= +4. 5. a) Find the amount s spent on advertising (in thousands of dollars) that maximizes the profit P (in thousands of dollars). b) Find the point of diminishing returns.6. 7. Simplify the expressions.a) 4132(5) (5)-� �� �� �b) 532ee-c) ( )( ) ( )0.13 1216 e8. Sketch the graph of the following functions.a) ( ) 5xf x = b) ( ) 3xg x e-=9.a) Use the model to estimate the sales in 2010 b) Use the model to estimate the sales in 201810. The current price of a car wash is $15. Use the model to estimate the price of a car wash in 10 years.11. On the day of a child’s birth, $500 is deposited in an account that pays 6% interest compounded continuously. Determine the balance in this account on the child’s 21st birthday.12. Given the formula for the effective rate of interest,1 1neffrrn� �= + -� �� �, find the effective rate correspondingto a nominal rate of 8.2% compoundeda) annually b) semi-annually c) quarterly d) monthly13. How much should be deposited now in an account paying 9.5% compounded quarterly in order to have a balance of 25000 in 15 years?14. The average time between incoming calls at a switchboard is 3 minutes. If a call has just come in, the probability that the next call will come within the next t minutes is P(t)=1−e−t3. Find the probability ofeach situation.a) A call comes within ½ minute.b) A call comes within 2 minutes.15. The cost of producing x units of a product is modeled by C=120+ 45 x−150 ln(x), x ≥1a) Find the average cost function, ´C.b) Find the number of units that will give a minimum average cost. (Round your answer to the nearest whole unit)16. Differentiate each of the functions.a) ( ) 3xg x e=b) ( )xg x e-= c) 23( ) 2xh x e-=d) 5( )xef xx=e) ( ) 2xh x xe=17. Write the equation of the line tangent to ( ) 1xf x e= + at the point (0, 2).18. 19. Solve for x. Round your answers to two decimal places.a)4 e2 x=12b)ln ⁡(x)=5c)(1.6)3 x=720. The population P (in thousands) of Phoenix, Arizona from 1980 to 2009 can be modeled by P=788 e0.0248t where t = 0 corresponds to 1980.a) What was the population in 2007?b) When will the population likely reach 3,000,000?21. Find the derivative of each of the following functions.a)f(x)=ln ⁡(4 x+1)b)y=53 x−7c)y=2 xln(x)22. Find an equation of the tangent line to the graph of f(x)=ln ⁡(x2) at the point (1,0).Answers:1a) 250 units b) 1000 units2. 158 units3a) $50 3b) $404a) $75 4b) $50.75 per unit5a) $10,000 5b) $5833.336) $1312.507a) 1015 ¿197656257b) 82e7c)1.5616e8a) 8b)9a) $73.13 billion b) $187.63 billion10. $22.20 11. $1762.7112a) 8.2% b) 8.3681% c) 8.4556% d) 8.5153%13. $6113.7114a) 0.1535 b) 0.486615a)´C=120x+45−150 ln ⁡(x )xb) $20.21 per unit16a) 3xeb) xe--c) 234xxe-d) ( )25 1xe xx-e) ( )2 1xe x + 17. y = x + 218a) $433.31 per year b) $890.22 per year c) $21839.26 per year19a) 0.55 b) 148.41 c) 1.3820a) 1,539,323 b) in 2033 or 203421a)44 x +1b)3(ln5)53 x−7c) 2+2ln ⁡x22. y = 2x –