1. Suppose that f is an exponential function with decay factor and that f 0

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1 Mh 1311 Homework 7 (Secion Secion 4.2) Record your nswers o ll he problems in he EMCF iled Homework Suppose h f is n exponenil funcion wih decy fcor nd h f Find formul for f x. ) f x x b) f x x c) f x x d) f x x 2. A cerin phenomenon hs iniil vlue 8 nd decys by 11% ech yer. Give n exponenil funcion h describes his phenomenon using vrible for ime in yers. ) 8 11 b) c) d) d 3. The exponenil funcion N , where d is mesured in decdes, gives he number of individuls in cerin populion. Find he yerly growh fcor (round o he neres housndh). ) b) c) d) The exponenil funcion , d N where d is mesured in decdes, gives he number of individuls in cerin populion. Find he percenge growh re (rounded o wo deciml plces) per cenury. ) 32.00% b) % c) % d) 16.06%

2 5. You iniilly inves $250 in svings ccoun h pys yerly ineres re of 5%, compounded nnully. Deermine how long i will ke for he ccoun o rech $ (ke ln or solve.) ) 5 yers b) 8 yers c) 9 yers d) 10 yers 6. Suppose cerin rdiocive subsnce hs hlf-life of 2 yers. Find how long i will ke for 400 grms of he subsnce o decy o 25 grms. ) 6 yers b) 8 yers c) 10 yers d) 12 yers 7. The yerly inflion re ells he percenge by which prices increse. In 1990 n individul reired on fixed income of $46,000 per yer. Assuming h he inflion re remins consn 9%, deermine how long i will ke in yers (rounded o he neres hundredh) for he reiremen income o defle o hlf is 1990 vlue. (Noe: To sy h reiremen income hs defled o hlf is 1990 vlue mens h prices hve doubled.) ) yers b) 7.35 yers c) yers d) 8.04 yers 8. Suppose counry hd populion of million in 1975 For he yers 1975 o 1985 he populion grew re of 4.9% per yer. Express in funcionl noion he populion of his counry in 1982 nd clcule h vlue (rounded o he neres hundredh). Assume he formul gives he populion N in millions of his counry wih respec o ime in yers from 1975 ) N(7) b) N(7) c) N(1982) d) N(7) 64.50

3 9. The exponenil funcion N = d where d is mesured in decdes, gives he number of individuls in cerin populion. Find he yerly growh fcor (round o he neres housndh). ) b) 1.41 c) d) Find formul for he exponenil funcion N N nd N 5 1. ) N /15 b) N 15 1/15 c) N 759,375 1/15 d) N 15 1/ 3375 using he informion N(2) Deermine wheher he following ble shows exponenil d or liner d. x y ) The d re liner. b) The d re exponenil. 12. For he exponenil funcion N N, incresing by 1 uni muliplies N by 0. How does n increse by 7 unis ffec N? ) 13 b) 42 c) 7 d) 84 6, where

4 13. In order o deermine is re of decy, 1 grm of n unknown rdiocive isoope ws plced in coniner. The moun remining ws mesured 1-minue inervls nd recorded in he ble below. Time (in minues) Grms remining Find n exponenil model for he d wih vrible M corresponding o remining mss (in grms) nd corresponding o ime (in minues). ) M b) M c) M d) M You hve invesed money in svings ccoun h pys fixed monhly ineres on he ccoun blnce. The following ble shows he ccoun blnce over he firs 5 monhs. Time (in monhs) Svings blnce 0 $ $ $ $ $ $ Find how long i kes for your money o double in vlue. ) yers b) 4.47 yers c) yers d) yers

5 15. The following ble shows he income, mesured in housnds of dollrs, from sles of cerin mgzine he sr of he given yer. Find n exponenil model for he income where I is he income, mesured in housnds of dollrs, nd is he number of yers since Round he prmeers o he neres hundredh. Yer Income ) I b) I c) I d) I Secion 4.1 Skill Building Exercise S-2 ) A = 4 X 8 b) A = 8 X 4 c) A = 10 X 7 d) A = 7 X Secion 4.1 Skill Building Exercise S-4 ) A = 0.7 X 25 b) A =.25 X 7 c) A = 25 X 0.7 d) A = 0.7 X. 25

6 18. Exercise 4.1 Skill Building Exercise S-6 ) A = 3 4 b) A = 7 10 c) A = 4 3 d) A = Secion 4.2 Skill Building Exercise S-2 ) 261% b) 60% c) 361% d) 61% 20. Secion 4.2 Skill Building Exercise S-4 ) 94% b) 6% c) 60% d) 96%