Question

Anyone here able to lend a helping hand?

Answer 1

Answer:

Step-by-step explanation:

1). Vertical intercept of the graph = Point at which the graph intersects the y-axis.

Therefore, vertical intercept is y = 1000.

In this situation vertical intercept means the initial dose of the drug taken = 1000 mg.

2). From the graph attached, point (x, y) represents,

x = Time 't' or duration

y = concentration of the drug after time 't'

Point (0, 1000) represents concentration = 1000 mg of the drug after t = 0 hour

Similarly, (1, 750) represents concentration = 750 mg after t = 1 hour

Therefore, fraction of drug remained = $\frac{750}{1000}$

                                                              = $\frac{3}{4}$

3). Let the equation, representing the concentration of the drug and time is,

$y=a(b)^t$

Here, a = Initial amount of the drug (at t = 0 hours)

            = 1000 mg

At (t = 1 hours), concentration of the drug = 750 mg

$y=1000(b)^t$

$750=1000(b)^1$

$b=\frac{750}{1000}$

$b=\frac{3}{4}$

Therefore, equation will be,

$y=1000(\frac{3}{4})^t$