Unit 7 Study Guide (2,25/16)

Transcription

1 Unit 7 Study Guide 1) The point (-3, n) eists on the eponential graph shown. What is the value of n? (2,25/16) (-3,n) (3,125/64) a)y = 1 2 b)y = 4 5 c)y = d)y = ) The point (-2, n) eists on the eponential graph as shown. If the function has the form y = ab + k, the value of n is: (-1,1) (-2,n) (0,-1)

2 3) The rabbit population in a forest area grows at the rate of 8% monthly. If there are 120 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be epected by net April. Use y = 120(2.7).08t Net April, the number of rabbits should be (round your answer to the nearest whole number). 4) Ray Industries bought a touch screen monitor for $850. The monitor is epected to depreciate at a rate of 35% per year. What will the value of the monitor be in 5 years? (Round to the nearest dollar) The value of the monitor in 5 years will be. (Choose one) $1148 $553 $3811 $99 5) Florist Company needs to determine to buy a new delivery van and wants to determine the value of the van after a certain number of years. Which function below represents the value of the new delivery van after years if the van initially costs $24,000 and depreciates 25% per year? b) y 24, d) y 24, a) y 25 24,000 c) y 24,

3 6) The graphs of eponential functions are given below. Match the graph on the right with it s the function at the top. f() = (3/2) f() = 2-3 f() =-2 f() =2 -

4 7) For the diagram below, figure b is a reflection of y = 3 in the line y = y = 3 y = b Which answer choice below is the equation for the graphed function, b, above? a) y 3 b) y 3 c) y log 3 d) y log 3 8) The graph of y=( 1 3 )+5 1 has which of the following? a) A vertical asymptote at = -5 b) A horizontal asymptote at y = -1 c) A vertical asymptote at y = -1 d) A horizontal asymptote at = -5 9) Which of the following choices is the inverse of f() = 5 +3? a) f -1 = log 3(-5) b) f -1 = log 5(-3) c) f -1 = 3 +5 d) f -1 = ) Which epression is equivalent to log 4 256? a) log 4 + log 256 b) log 4 log 256 c) (log 4)(log 256) d) log256 log4

5 11) Which answer choice below is the equation 16 2 = 124 in logarithmic form? a) = log62 log256 b) = log256 log62 c) = 2log124 log16 d) = log124 log256 12) Use the properties of logarithms to epand the logarithm epression log b(z 5 ) as much as possible. a) log b + log b 5z b) 5log b + 5log b z c) log b + 5log b z d) 5log b z 13) The function S(d)= 500 log d relates S(d), the speed of the wind near the center of a tornado in miles per hour, to d, the distance that thee tornado travels in miles. If winds near the center reach speeds of 750 mph, estimate the distance the tornado can travel. The estimated distance the tornado can travel is.

6 14) Describe the strategy you would use to solve log 3 = log log 3 8. a) Epress the equations in the eponential form, set the eponents equal to each other, and solve. b) Use the fact that the logs have the same base to add the epression on the right side of the equation together. Epress the results in eponential form, set the eponents equal to each other, and solve. c) Use the product rule to turn the right side of the equation into a single logarithm. Recognize that the resulting value is equal to. d) Use the fact that since both sides of the equation have logarithms with the same base set the epressions equal to each other and solve. 15) Describe how the graph of the function y=3-2 is related to the graph of its parent function. Then find the domain, range, and asymptotes. a) y=-3 translated up 2 units. b) y=3 translated up 2 units. Domain: >2 Range: All real numbers Range: All real numbers Vertical asymptote: =2 No asymptote c) y=3 reflected over the -ais translated down 2 units d) y=3 translated down 2 units. Range: y>-2 Range: y>-2 Horizontal asymptote: y=-2 Horizontal asymptote: y=-2 16) Describe how the graph of the function y=-(2) +5 is related to the graph of its parent function. Then find the domain, range, and asymptotes. a) y=2 reflected about the y-ais and translated 5 units left. Range: y>0 Horizontal asymptote: y=1 b) y=2 reflected about the -ais and translated 5 units left. Range: y<0 Horizontal asymptote: y=0 c) y=2 reflected about the -ais and translated 5 units right. Range: y<0 Horizontal asymptote: y=-1 d) y=2 reflected about the y-ais and translated 5 units right. Domain: <0 Range: all real numbers No asymptote

7 17) Write the equation e 5 = in logarithmic form. a) ln(5) = b) ln(148.41) = 5 c) ln(5) = e d) ln(148.41) = e 18) Use the properties of logarithms to evaluate the epression 2log log The epression 2log log =. 19) Use the change of base formula to rewrite the epression log 13 8 using common logarithms. a) log13 log8 b) log8 log13 c) log 8 log13 d) log 13 log8 20) Bill has $10,000 and is going to invest in an account that has an 8% continuously compounded interest rate. Bill is hoping to have $20, 000 for a down payment to buy a home. How long would Bill have to wait before his investment reaches $20,000? Use the formula A = Pe rt where A is the balance at time t, P is the principal and r is the interest rate.

8 21) Match equation with its equivalent form. Place X in the appropriate bo. log 310 = ln 3 = log 5 = ln = 3 3 = 10 e = 3 e 3 = 10 =5 22) Determine the solution to the eponential function, 9 4 = 27. A. 8 3 B. 3 4 C. 3 8 D. 2 23) Solve log 4 + log 15 = 1. Round to the nearest hundredth if necessary. A. 24 B C D. 600