An element with mass 510 grams decays by 26.3 percent per minute. How much of the element is remaining after 7 minutes, to the nearest 10th of a gram?
We can solve this problem using exponential decay. The amount remaining at any given time $t$ can be modeled by the equation $A(t) = A_0(1-r)^t$, where $A(t)$ is the amount remaining at time $t$, $A_0$ is the initial amount, $r$ is the decay rate, and $t$ is time in minutes.
In this problem, the initial amount $A_0$ is 510 grams, the decay rate $r$ is 26.3%, or 0.263 as a decimal, and we want to find $A(7)$.
Plugging in the given values, we have:
$A(7) = 510(1-0.263)^7$
Calculating this expression, we find:
$A(7) \approx 510(0.737)^7 \approx 261.0$
Therefore, after 7 minutes, approximately 261.0 grams of the element remain. Rounding to the nearest tenth of a gram, the answer is $\boxed{261.0}$ grams.