An element with mass 570 grams decays by 26.9% per minute. How much of the element is remaining after 14 minutes, to the nearest 10th of a gram?

Accepted Solution

Answer:7.1Step-by-step explanation:Exponential Functions: y=ab^x y=ab  x  a=\text{starting value = }570 a=starting value = 570 r=\text{rate = }26.9\% = 0.269 r=rate = 26.9%=0.269 \text{Exponential Decay:} Exponential Decay: b=1-r=1-0.269=0.731 b=1−r=1−0.269=0.731 \text{Write Exponential Function:} Write Exponential Function: y=570(0.731)^x y=570(0.731)  x  Put it all together \text{Plug in time for x:} Plug in time for x: y=570(0.731)^{14} y=570(0.731)  14  y= 7.091174 y=7.091174 Evaluate y\approx 7.1 y≈7.1 round