Question

Country A has a growth rate of 3.23.2​% per year. The population is currently 4 comma 4334,433​,000, and the land area of Country A is 3434​,000,000,000 square yards. Assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

Answer 1

Given :

The growth rate of the country = r = 3.232 %

Current population = p = 4,4334,433,000

The land area available = A = 3434,000,000,000  sq yard

To Find :

Time after which one sq yd available per person = T years

Solution :

Available land area = current population × $(1+\dfrac{rate}{100})^{time}$

Or, 3434,000,000,000  sq yard =  4,4334,433,000  × $(1+\dfrac{3.232}{100})^{T}$

Or, $(1+\dfrac{3.232}{100})^{T}$  = $\dfrac{3434000000000}{44334433000}$

Or,  $(1.03232)^{T}$ = 77.45

Now, Taking Log with base 10 both side

So,  Log$(1.03232)^{T}$ = Log 77.45

Or,  T Log 1.03232 = Log 77.45          ( from log property $Log_ab$ = b Log a )

Or, T × 0.01381 = 1.889

∴                    T = $\dfrac{1.889}{0.01381}$

i.e            Time  = 136.7 ≈ 138    years

So, The Time after which one sq yd available per person = T =138 years

Hence, The Time after which one sq yd available per person is 138 years Answer