Question

A population of endangered birds decreases by 3% each year.

Answer 1

Since the number of bird decreases 3% per year then for year 1 there will be 29 100 birds left. This value is 97% of 30000. From this the number of birds for year 1 is N = 30000(1-0.03)

A. N = 30,000$(1-0.03)^{2}$

B. To solve this we use the equation we established in letter A. We get the answer by substituting T with 20. N = 16,000. <span />

Answer 2

Answer: a) The required equation is,

$N=30000(0.97)^T$

b) The approximately population of the birds after 20 years is 16314.

Step-by-step explanation:

a) Since, the initial population, P = 30,000

The rate of increasing, r = 3% per year,

Hence, the population of birds after T years,

$N=P(1-\frac{r}{100})^T$

$\implies N = 30000(1-\frac{3}{100})^T$

$\implies N = 30000(1-0.03)^T$

$\implies N=30000(0.97)^T$

Which is the required equation.

b) Now, for T = 20 years,

The population of birds,

$N(20)=30000(0.97)^{20}=30000\times 0.543794342927=16313.8302878\approx 16314$

⇒ The approximately population of the birds after 20 years is 54183.