Question

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

Answer 1

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.
 

Answer 2

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.