Question

Substance A decomposes at a rate proportional to the amount of A present. It is found that 8 lb of Awill reduce to 4 lb in 4.5 hr. After how long will there be only 1 lb left There will be 1 lb left after hr. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Answer 1

Explanation is in the following pictures !

Final Answer is :- 13.5 hrs

solution of Say Amount at any Instant of Lets time time ta 2. t. be that o- to So It it given decom position rate is pooportional the amount of a present. As we know decomposition rate can be given by dt, Condition. So, given According to the da azt da ka ok constant of proportionality This is first order Linear differenti al équation, da at Scanned with Camseparate the variables CS

Kdt - da → Now wil can Integrate It Limits of Integration :- At (34) = 816. time t =0 (Initial time) Amount of A At time Amount of A =T and So, Integrate f kat 8 X (11 dx = lox anbul kt 6 en X en 8 KT – D. isen m. - KT en emon) It is given ven that In 4.5 hr. Amount has been reduced From 8 Lb to 4 Lb cs Scanned with x = 4 CamScanner and t=4.5

at which we can find time I So, of A will be 1 lb.. So, put x = Amount o en (1) I en I 8 4.5 2 ln (1/6) T = 45 ln (1/2). T= 4.5 ln (2) ha 23 en 12 T = 4.5(3) ly T en 12 tog mlega T T = 4.5 (3) 13.5 hours Answer So, After 13.5 hours there will be only Left , amount Cs Scanned Milib of CamScanner
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