The variation in size from year to year of a particular population can be
modelled by an exponential model with annual proportionate growth rate
0.1246. The size of the population at the start of the initial year is 360.
Choose the TWO options that give, as predicted by the model,
(a) the population size after 10 years;
(b) the number of years for the population size to reach at least 2500.
Options
A 15 B 17 C 20 D 24
E 849 F 1035 G 1165 H 1310
To answer this question, we need to use the exponential growth formula:
N(t) = N₀ * e^(r * t)
Where:
N(t) is the population size at time t
N₀ is the initial population size
r is the annual proportionate growth rate
e is the base of the natural logarithm
t is the time in years
(a) The population size after 10 years:
We can use the given information to calculate the population size after 10 years using the exponential growth formula.
N(10) = 360 * e^(0.1246 * 10)
To find the result, you can use a scientific calculator or an online calculator that has an exponential function. After calculating, you will get the population size after 10 years.
(b) The number of years for the population size to reach at least 2500:
We need to find the value of t when N(t) is equal to or greater than 2500. Rearranging the exponential growth formula, we get:
2500 = 360 * e^(0.1246 * t)
Again, to find the value of t, you can use a scientific calculator or an online calculator that has an exponential function.
By substituting the given options, you can determine which ones give the predicted values for (a) and (b) as calculated above.