Question

the doubling time of a population of flies is 8 hours. by what factor does the population increase in 33 hours? by what factor does the population increase in 2 weeks?

by what factor does the population increase in 33 hours?
\\(2^{4.125}\\)
(type exponential notation with positive exponents. use integers or decimals for any numbers in the expression.)

by what factor does the population increase in 2 weeks?
(type exponential notation with positive exponents. use integers or decimals for any numbers in the expression.)

Explanation:

Formulate the exponential growth model

Using the Exponential Growth and Doubling Time knowledge points

$$ P(t) = P_0 \cdot 2^{t / T_d} $$

$$ T_d = 8\text{ hours} $$

$$ \text{Growth factor } F(t) = 2^{t / 8} $$

Calculate the growth factor for 33 hours

Using the Doubling Time knowledge point

$$ t = 33\text{ hours} $$

$$ F(33) = 2^{33 / 8} = 2^{4.125} $$

Convert 2 weeks into hours

Using the Doubling Time knowledge point

$$ t = 2\text{ weeks} \times 7\text{ days/week} \times 24\text{ hours/day} $$

$$ t = 336\text{ hours} $$

Calculate the growth factor for 2 weeks

Using the Doubling Time knowledge point

$$ F(336) = 2^{336 / 8} = 2^{42} $$

Answer:

Question 1

By what factor does the population increase in 33 hours?
<blank>\(2^{4.125}\)</blank>

Question 2

By what factor does the population increase in 2 weeks?
<blank>\(2^{42}\)</blank>