Question

$z^{2}+10z - 24 = 0$
what is one of the solutions to the given equation?
your answer
15 *
15
bacteria are growing in a liquid growth medium. there were 300,000 cells per milliliter during an initial observation. the number of cells per milliliter doubles every 3 hours. how many cells per milliliter will there be 15 hours after the initial observation?
a
b
c
d
a

Explanation:

Step1: Factor the quadratic equation

We find two numbers that multiply to $-24$ and add to $10$: $12$ and $-2$.
$z^2 + 10z - 24 = (z + 12)(z - 2) = 0$

Step2: Solve for $z$

Set each factor equal to 0:
$z + 12 = 0$ or $z - 2 = 0$
$z = -12$ or $z = 2$

Step1: Calculate doubling periods

Number of doubling cycles: $\frac{18}{3} = 6$

Step2: Compute final cell count

Use exponential growth formula: $N = N_0 \times 2^n$, where $N_0 = 300000$, $n=6$
$N = 300000 \times 2^6 = 300000 \times 64$

Step3: Calculate the product

$300000 \times 64 = 19200000$

Answer:

$z = 2$ (or $z = -12$ is also a valid solution)

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For the bacteria growth problem (Question 15, note: the doubling time is partially obscured, assuming it is 3 hours as 18 is a multiple of 3, a common setup):