Question

exponential functions - basic
question
an element with mass 330 grams decays by 25.5% per minute. how much of the element is remaining after 5 minutes, to the nearest 10th of a gram?
answer
attempt 1 out of 2

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time.
Here, $P = 330$ grams, $r = 25.5\% = 0.255$, and $t = 5$ minutes.

Step2: Substitute values into the formula

Substitute $P = 330$, $r = 0.255$, and $t = 5$ into the formula:
$A = 330(1 - 0.255)^5$
First, calculate $1 - 0.255 = 0.745$.
Then, calculate $0.745^5$. Let's compute that:
$0.745^5 \approx 0.745 \times 0.745 \times 0.745 \times 0.745 \times 0.745$
$0.745^2 = 0.555025$
$0.745^3 = 0.555025 \times 0.745 \approx 0.4135$
$0.745^4 = 0.4135 \times 0.745 \approx 0.3081$
$0.745^5 = 0.3081 \times 0.745 \approx 0.2295$

Now, multiply by $330$:
$A = 330 \times 0.2295 \approx 75.735$

Step3: Round to the nearest tenth

Rounding $75.735$ to the nearest tenth gives $75.7$.

Answer:

$75.7$