Answer:
The equation that will represent the number of grams present after n hours is [tex]A(n) = 150(0.85)^n[/tex]
3.035 grams will be left one day from now.
Step-by-step explanation:
Exponential equation for the amount of a substance:
The exponential equation for the amount of a substance is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time period.
A radioactive isotope is decaying at a rate of 15% every hour.
This means that [tex]r = 0.15[/tex]
Currently there are 150 grams of the substance.
This means that [tex]A(0) = 150[/tex]
Write an equation that will represent the number of grams present after n hours.
[tex]A(n) = A(0)(1-r)^n[/tex]
[tex]A(n) = 150(1-0.15)^n[/tex]
[tex]A(n) = 150(0.85)^n[/tex]
How much will be left one day from now?
One day is 24 hours, so this is A(24).
[tex]A(24) = 150(0.85)^{24} = 3.035[/tex]
3.035 grams will be left one day from now.
