The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.

Which function can be used to determine the approximate number of grams of the sample remaining after t hours?

a

y = 50(0.85)x

b

y = 25(0.15)x

c

y = 50(0.15)x

d

y = 25(0.85)x

I can't see how any of those formulas show exponential decay. (Did you type those correctly?)

The formula that will show the remaining amount correctly is:
ending amount = Bgng Amount / 2^n
where "n" is the number of haf-lives.

So, for example if half life = 4 hours and if we want to calculate the amount after 9 hours (that's 2.25 half-lives) then:
ending amount = Bgng Amount / 2^n
ending amount = 50 / (2^(9/4))
ending amount = 50 / 2^2.25
ending amount =
50 / 4.75682846

ending amount =

10.5112 grams
Looking at the graph, we see that's about right.

parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-02-25T07:28:04-05:00

Answer:

a) \(y = 50(0.85)^x\)

Step-by-step explanation:

Let the function that shows the given situation is,

\(y=ab^x\)

Where a and b are any unknown numbers,

By the given diagram,

When x = 1, y = 42.5,

\(\implies 42.5 = ab^1\)

\(\implies ab = 42.5\) ------(1)

Again, when x = 4, y = 26,

\(\implies 26 = ab^4\)

\(\implies 26 = ab(b^3)\)

\(\implies 26 = 42.5(b^3)\) ( By equation (1) )

\(\implies 0.611764706 = b^3\)

\(\implies 0.84890965425 = b\)

Again, By equation (1),

a = 50.0642203646

Hence, the equation that shows the given graph,

\(y = 50.0642203646(0.84890965425)^x\)

\(\implies y = 50(0.85)^x\)

⇒ Option a is correct.