Question

4. Paige cultured 100,000 paramecium (unicellular). Ten days later, the population grew to 500,000 paramecium cells. Calculate the intrinsic rate of increase (r) for her population. (Show all calculations to receive any credit) (10) 5. For the above paramecium population (Q.4) above, use the exponential model of population growth to predict the size of the population after another 10 days. (Show all calculations to receive any credit) (10)

Answer 1

QUESTION-4

ANSWER-

Paige cultured 100,000 unicellular parameciums.

Ten days later, the population grew to 500,000 paramecium cells.

Now we have to calculate the intrinsic growth rate (r)-

We know that,

Nt = N₀ e^rt

where,

N_t= final population size at the time t

N₀= initial population size

r= Intrinsic growth rate

t= time

N_t = N₀ e^rt

N_t$\div$ N₀ = e^rt

Let's take the natural log of both the sides to get rid of e-

ln(N_t$\div$ N0) = ln e^rt

lnN_t - ln  N₀= rt

r= lnN_t - ln  N₀$\div$ t

Provided information-

N_t= 500,000

N₀ = 100,000

t= 10 days

Now put these values in the above equation-

r= ln (500,000) - ln (100,000) $\div$ 10

r= 13.12- 11.51 $\div$ 10

r= 1.13$\div$10

r= 0.113

CONCLUSION- The intrinsic growth rate is 0.113.

GOOD LUCK.