An exponential function is a function defined by y = ab^x, where a represents the initial value, and b represents the rate
(a) The factor at which the medicine decreased, in 1.5 hour
From the graph, we have the following ordered pairs
(x,y) = (0,270) and (1.5,80)
Given that:
[tex]y = ab^x[/tex]
At point (0,270), we have:
[tex]ab^0=270[/tex]
[tex]a= 270[/tex]
At point (1.5,80), we have:
[tex]ab^{1.5} = 80[/tex]
Substitute 270 for a
[tex]270b^{1.5} = 80[/tex]
Divide both sides by 270
[tex]b^{1.5} = 0.2963[/tex]
Take 1.5th root of both sides
[tex]b =0.44[/tex]
Hence, the medicine decrease in the hour and half at a factor of 0.44
(b) The factor at which the medicine decreased in the first half hour, and the first hour
In (a), we have:
The decay factor (b) to be 0.44
This represents the factor at which the medicine decreased throughout.
Hence, the medicine decrease in the first half hour, and the first hour at a factor of 0.44
(c) The exponential equation
In (a), we have:
[tex]a= 270[/tex]
[tex]b = 0.44[/tex]
So, the exponential equation is:
[tex]y =270 * 0.44^x[/tex]
In terms of m and h, we have:
[tex]m =270 * 0.44^h[/tex]
Hence, the equation relating m to h is [tex]m =270 * 0.44^h[/tex]
Read more about exponential equations at:
https://brainly.com/question/11832081
