Question

The population of big cats in Africa is increasing at a rate of 5% per year. At the

Answer 1

Answer:

a) 10,500 big cats

b) 13,401 big cats

c) 33 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:  

A = P (1 + r) t  

Where:  

p = original population  

r = growing rate (decimal form; 5/100= 0.05)

t= years  

A = population after t years  

Replacing with the values given:  

a) At 2005, 1 year passed since 2004 (t=1)

A = 10,000 (1+ 0.05)^1

A = 10,500 big cats

b)

At 2010, 6 years passed since 2004 (2010-2004= 6)

A = 10,000 (1+ 0.05)^6

A = 13,401 big cats

c)

50,000 < 10,000 (1+ 0.05)^t

Solving for t:

50,000/10,000 < 1.05^t

5 < 1.05^t

log 5 < log 1.05^t

log 5 < t ( log 1.05)

log 5 / log 1.05 < t

32.9 years < t

33 years  = t

Feel free to ask for more if needed or if you did not understand something.