Using the concept of exponential growth and exponential decay, solve the given problem. Show complete and systematic solutions. 1. An unknown radioactive element decreases 12% of its amount every 5 days. What is exponential function? that describes the amount left after t days? If there are 300g of the substance at present, how much is left after 30 days? (round off the value up to two decimal places)

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Using the concept of exponential growth and exponential decay, solve the given problem. Show complete and systematic solutions.    1. An unknown radioactive element decreases 12% of its amount every 5 days. What is  exponential function? that describes the amount left after t days? If there are 300g of the  substance at present, how much is left after 30 days? (round off the value up to two decimal  places)

logik4z · Accepted Answer

Given thatradioactive element decreases 12 % of its amount every 5 days. amount of substance at present is 300 g We have to find exponential function left after t days. Exponential function for radioactive decay is P(t)=Poekt−(1) where t is time Po= amount at present P(t)=amount after time t k= constant herePo=300g, t=5 days after 5 days radioactive amount decreases 12 % that is P(t)= 300x(100−12)100=3×88 P(t)=264 g Now put these value in (1) 264=300e5k Now we find constant K 264=300e5k 264300=e5k 6675=e5k taking In both of sides we get In(6675)=Ine5k In(6675)=5Kln⁡e ln⁡(6675)=5k [∴ln⁡e=1] -0.12783372=5k ⇒k=−0.127833725 ⇒k=−0.0255666744 eqn(1) become P(t)=300e−(0.0255666744)t this describe amount left t days. P(t)=300e−(0.0255666744)t amount left after t=30 days P(t)=300e−(0.0255666744)x30 P(t)=300e−0.767000232 P(t)=300(0.464404085) P(t)=139.32 g amount left after 30 days is 139.32 g

Using the concept of exponential growth and exponential decay, solve the given problem. Show complet

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