9.8 is the middle number which is the median
We find the value of N₀ since we are provided with initial conditions.
The condition is that, at time t = 0, the amount of substance contains originally 10 grams.
We substitute:
10 = N₀ (e^(-0.1356)*0)
10 = N₀ (e^0)
N₀ = 10
When the substance is in half-life (meaning, the half of the original amount), it contains 5 grams. We solve t in this case.
5 = 10 e^(-0.1356*t)
0.5 = e^(-0.1356*t)
Multiply natural logarithms on both sides to bring down t.
ln(0.5) = -0.1356*t
Hence,
t = -(ln(0.5))/0.1356
t ≈ 5.11 days (ANSWER)
The equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
<h3>How to determine the equivalent expression?</h3>
The expression is given as:
x^3 (x^2 + 5x + 7)
Expand the expression
x^3 * x^2 + x^3 * 5x + x^3 * 7
Evaluate the product
x^5 + 5x^4 + 7x^3
Expand the expression
x^5 + 4x^4 + x^4 + 8x^3 - x^3
Hence, the equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
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Let's say that Stan invested $1500 at 6%. To find how much he invested at 4.5% would be 5000 - 1500 = $3500. Now we have a pattern. Now let's say stan invested x dollars. Even though it is unknown, we can set up how much is left. So subtract x from 5000 or 5000 - x which is C
