An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

There will be 38 grams remaining.

The equation would be of the form
y = a(1+r)ˣ, where a is the initial value, r is the rate as a decimal number, and x is the amount of time. Using our values from the problem, we have:

y = 670(1-0.273)^9 = 670(0.727)^9 = 38

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-06-19T17:18:48+02:00

Answer: 38.0 grams

Step-by-step explanation:

The exponential decay equation with rate of decay r in time period x is given by :-

[tex]f(x)=A(1-r)^x[/tex], A is the initial value .

Given: The initial mass of element= 670 grams

Rate of decay= 27.3%=0.273

Now, the function represents amount of element after x minutes is given by ;-

[tex]f(x)=670(1-0.273)^x\\\\\Rightarrow\ f(x)=670(0.727)^x[/tex]

Now, the function represents the amount of element after 9 minutes is given by ;-

[tex]f(x)=670(1-0.273)^9\\\\\Rightarrow\ f(x)=38.0088299313\approx38.0\text{ grams}[/tex]

Hence, 38.0 grams of element remains after 9 minutes.