Question

1. simplifying expressions (a-sse.4, f-e.4)

rewrite the following expression in an equivalent form using properties of exponents:

\\\frac{3e^{2x} \cdot e^{3x}}{9x^x}\\

1. writing an exponential model (f-le.4.1, f-bf.4)

a bacteria culture starts with 500 bacteria and doubles every 3 hours.

a) write an exponential function representing the number of bacteria after \\(t\\) hours.

b) how many bacteria will there be after 12 hours?

Explanation:

Simplify the numerator of the expression in Question 1

$$ 3e^{2x} \cdot e^{3x} = 3e^{2x + 3x} = 3e^{5x} $$

Divide by the denominator to find the simplified form for Question 1

$$ \frac{3e^{5x}}{9x^x} = \frac{e^{5x}}{3x^x} $$

Formulate the exponential growth function for Question 2a

$$ N(t) = 500 \cdot 2^{\frac{t}{3}} $$

Calculate the bacteria population after 12 hours for Question 2b

$$
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$$

Answer:

Question 1

$$ \frac{e^{5x}}{3x^x} $$

Question 2

a) \(N(t) = 500 \cdot 2^{\frac{t}{3}}\)

b) \(8000\) bacteria