UNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS
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1 Answer Key Name: Date: UNIT # EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS Part I Questions. Te epression 0 can be simpliied to () () 0 0. Wic o te ollowing is equivalent to () () 8 8? 8. I 0 ten wic o te ollowing represents te value o 0? () () (). Wic o te ollowing is te equation o an increasing eponential unction? y () y () 0.7 y 7 y Coices () and are not eponential unctions. Coices () and are. An eponential unction will always increase wen its base is greater tan. Since / is greater tan, tis eponential increases.. I Jordan ad is ourly salary increase rom $. per our to $0.7 per our, wic o te ollowing is closest to te percent increase in Jordan's salary? () 8% () % % % Jordan's Pay Increased $0.7 $. $.0.0 Percent Increase 00.%. () COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0
2 . Wic o te ollowing could be te equation o te eponential unction sown below? () y 0. y 7. () y 80. y. 0 y Tis is a decreasing eponential wose y- intercept is somewere between and 0. In te general orm o an eponential y ab, a is te y-intercept and b, te base, indicates increasing and decreasing. In tis case, since te eponential decreases, b must lie between 0 and. So only Coice () as a reasonable y-intercept and is decreasing. () 7. Te population o Ketcam Hig Scool as been decreasing by % per year. I its population is currently,00 students, wic o te ollowing is closest to its population two years rom now? (),0 (),70,7, A population o bacteria is increasing at a rate o 7.% per our. I tere were originally 7 bacteria, wic o te ollowing equations models te population o bactera -ours ater te original 7 bacteria were measured? () 77. P () P.07 7 P 7.7 P 7.07 Since te population starts at 7, tat is its y-intercept (or a value). Te multiplier, or base, is always +%, were te percent is epressed in decimal orm. So: P I te irst two terms o a geometric sequence are and, wic o te ollowing would be te 0 t term? () 7 () 78,7 8, Geometric series increase (or decrease) by constant multiples. In tis case te common multiplier (or ratio) is. To get te 0t term, recall, you only multiply by -times: a0,8 78,7 0. A radioactive material as a mass given by mt 0.8 t, were te mass is in grams and te time, t, is in years. Wic o te ollowing gives te average rate o cange o te mass over te interval t years? m 88.0 grams (). grams per year m.7 grams. grams per year m m.7 grams 88.0 grams () 8. grams per year years years () 8. grams per year.0 grams.070 grams per year years COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0 ()
3 Free Response Questions. Simpliy te ollowing epression. Write it in two ways, one wit te use o negative eponents and one wit te use o a raction (tat doesn't ave negative eponents).. Simpliy te ollowing epression.. An object's speed can be modeled wit te equation S.0 t, were S represents its speed in miles per our and t represents te amount o time tat as passed, in seconds. Give an interpretation o te parameters and.0 rom te equation. In an eponential unction o te orm y a b, te a always represents te original quantity and te b indicates te percent increase or decrease. So, te means te object was initially moving at miles per our. Te.0 means its speed was increasing at % per second.. An eponential unction,, is sown in te table below. Determine an equation or it in ab orm. 0 7 Our a-value will be te y-intercept, or. Te b represents ow muc we multiply by or eac unit increase in. From te table we can tell tis is. COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0
4 . Ma deposits money into a savings account tat earns.% interest applied annually. I Ma initially deposits $0 into te account, ow muc money does te account old ater -years i Ma does not deposit or witdraw any additional money? Sow ow you arrived at your answer $ $.. Determine te equation o te eponential unction sown graped below. Eplain ow you arrived at your answer. Create a list o values: 0 y 0 y y. Te y-intercept is 0 and we are clearly dividing by or eac unit increase in. So, our equation is: y 0 or y A unction passes troug te points 0, 8 and,. (a) Write te equation o a linear unction tat passes troug tese two points and write te equation o an eponential unction tat passes troug tese two points. Linear, y m b Eponential, b 8 8 m 0 y 8 a 8 b 8 8 y y a b (b) How muc greater is te eponential unction's value at tan te linear unction's value? Sow ow you arrived at your answer. Linear: y 8 y 8 88 Eponential: y 8 y 8, Te eponential is:, 88, 8 greater tan te linear. COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0
5 8. A geometric sequence is deined using te ollowing rule: 0 and n n Find te ourt term o te sequence. Sow ow you arrived at your answer Wic is larger, te 0t term o an aritmetic sequence tat begins wit te terms 0 and 00 or te 0t term o a geometric sequence tat begins wit te terms and 0? Sow work tat justiies your answer. From te irst two terms o te aritmetic sequence, we can tell tat we need to add 00 to get eac term, so te 0t term would be: a From te irst two terms o te geometric sequence, we can tell tat we need to multiply by to get eac term, so, te 0t term would be: a 0,0 Te eponential sequence as te larger 0t term. 0. A local newspaper claims tat te number o lu cases is increasing eponentially. On Monday, tere were 8 lu cases reported. On Tuesday, tere were lu cases and on Wednesday tere were cases reported. On Tursday, tere were 0 lu cases. Was te newspaper's claim o eponential increase accurate? Justiy your response. I tis is truly an eponential increase in te number o cases, ten te ratio o eac successive pairs o outputs will remain constant: No, tis is not eponential increase since te ratio is not a constant.. Te irst tree terms o a geometric sequence are sown below. Write a recursive rule or tis sequence.,, We need to determine te constant multiplier or ratio or tis geometric sequence. We need to be careul because it is a decreasing eponential. Te ratio can be ound by: 0. a a n an Wat is te net term o te sequence? a a COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0
UNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS
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