Question

In the year 2000, China was the worlds most populous country with an estimated population of 1.26 billion people. The second most populous country was India with 1.01 billion. The populations of India and China can be modeled by I(t)= 1.01e^0.015t and C(t)= 1.26e^0.009t, respectively. According to these models one more India's population be more than China's?

Answer 1

To know when will India´s population exceed China´s we need to know  

when will they be equal. So:

$I(t)=C(t)$

$1.01e^{0.015t}= 1.26e^{0.009t}$

We apply logarithm´s law to both sides:

$ln (1.01e^{0.015t})= ln (1.26e^{0.009t})\\ ln (1.01) + ln (e^{0.015t})= ln (1.26) +ln(e^{0.009t})\\ ln (1.01) + 0.015t= ln (1.26) +0.009t\\ 0.015t-0.009t= ln (1.26) - ln (1.01) \\ 0.006t= (ln (1.26) - ln (1.01))\\t=(ln (1.26) - ln (1.01))/0.006$

So t=36.860231685

this means that India´s population will exceed China´s in year 2036