Question

Initially, we have 200 g of a radioactive substance. If the mass of the substance is decaying by 7% per day. What will be the population after 8 days?

Answer 1

200 * 0.93^8 = ____

Answer 2

may I ask where did the 0.93 come from?

Answer 3

7% loss means it assumes 93% of its former value

Answer 4

[AI-generated answer — Explain Bot]

To calculate the population of the radioactive substance after 8 days, we need to apply the decay formula. The formula for exponential decay is:

N = N₀ × e^(kt)

Where:
N = Final population (unknown)
N₀ = Initial population (200 g)
k = Decay constant (0.07, expressed as a decimal as the substance is decaying by 7%)
t = Time in days (8 days)
e = Euler's number (approximately 2.71828)

Let's substitute the given values into the formula:

N = 200 × e^(0.07 × 8)

First, calculate the exponent:

0.07 × 8 = 0.56

Next, calculate e^(0.56). The value of e^(0.56) is approximately 1.75465.

Finally, multiply:

N = 200 × 1.75465

N ≈ 350.93

Therefore, the population of the radioactive substance after 8 days will be approximately 350.93 grams.