Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

look at c

25 = 100(0.5)^1

does that work..?

Answer 5

yes.

Answer 6

so 100 * 0.5 = 25...?

Answer 7

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.

Answer 8

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.

Answer 9

@campbell_st