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Mathematics 13 Online
OpenStudy (anonymous):

Help w. algebra please :) Will award fan and medal!!!

OpenStudy (anonymous):

The amount of radioactive uranium changes with time. The table below shows the amount of radioactive uranium f(t) left after time t: t(hours) 0 0.5 1 f(t) 100 50 25 Which exponential function best represents the relationship between f(t) and t? f(t) = 100(0.25)t f(t) = 0.25(100)t f(t) = 100 (0.5)t f(t) = 0.25(50)t

OpenStudy (anonymous):

i believe it is either c or d am i right??? :)

OpenStudy (campbell_st):

well an easy thing is to substitute f(1) = 25 that is x = 1 and f(x) = 25 into each equation to find the correct one.

OpenStudy (campbell_st):

look at c 25 = 100(0.5)^1 does that work..?

OpenStudy (anonymous):

yes.

OpenStudy (campbell_st):

so 100 * 0.5 = 25...?

OpenStudy (campbell_st):

you are also told that the initial amount is 100 so x = 0 and f(x) = 100 so then you can use this as a secondary check.

OpenStudy (campbell_st):

any simple exponential growth model is in the form \[f(x) = P_{0} \times a^n\] where \[P_{0} = Initial ~~amount\] so in your model \[P_{0} = 100\] so that eliminates 2 choices as the model becomes \[f(x) = 100 \times a^x\] so to find a, use some information from the table. the easiest is f(x) = 25 and x = 1 substitute them and then solve for a to find the correct model.

OpenStudy (anonymous):

@campbell_st

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