Question

5. Use your answers to questions 3 and 4 to write an expression for how many times greater organism B's population is than organism A's population after 8 days. Simplify your expression, then write it as a number that is not in exponential form. Show your process. Write your answer in the space below. My answer​

Answer 1

Population growth represents the rate at which the population changes

• The expression for the number of times the population of B is greater than A is: $2^6$
• The expression that is not in exponential form is: 64

Given that:

$r_1 = 2$ ----- i.e. when the population doubles

$r_2 = \frac{1}{2}$ ----- i.e. when the population cut in halves

Population growth is represented as: $A_n = ar^{n}$

Organism A

For the first 5 days (when it doubles) is:

$A_5 = ar_1^{5$

Substitute $r_1 = 2$

$A_5 = a\times 2^{5$

For the next 3 days (when it cut in halves) is:

$A = A_5 \times r_2^3$

Substitute $A_5 = a\times 2^{5$ and $r_2 = \frac{1}{2}$

$A= a \times 2^5 \times (\frac{1}{2})^3$

Apply law of indices

$A = a \times 2^5 \times 2^{-3$

$A = a \times 2^{5-3$

$A = a \times 2^{2$

So, the growth factor of organism A is:

$A = a \times 2^{2$

Organism B

For the 8 days, we have:

$B=ar_1^8$

$B=a\times 2^8$

The expression (n) for the number of times the population of B is greater than A is:

$n = \frac BA$

This gives:

$n = \frac{a \times 2^8}{a \times 2^2}$

$n = \frac{2^8}{2^2}$

Apply law of indices

$n = 2^{8-2}$

$n = 2^{6}$

The expression that is not in exponential form is:

$n = 2 \times 2\times 2\times 2 \times 2\times 2$

$n = 64$

Hence:

• The expression for the number of times the population of B is greater than A is: $2^6$
• The expression that is not in exponential form is: 64

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