can someone help me with this question The general function

can someone help me with this question

The general function P(t)=P(initial)e^(kt) is used to model the size of a bird population, where the time t is measured in years. Suppose there are initially 630 birds. After 3 years there are 1050 birds. Find the exact time it will take for the bird population count to grow to four times its initial size. Simplify your answer.

Solution

P(t)= p*e^(kt)

1050=630 e^(k*3)

1050/630=e^(3k)

Taking ln on both sides

ln(1050/630)/3=k

now the population grows to 4 times. Therefore if initially it is 630,then after t it becomes 4*630=2520

2520=630 e^(t*ln(1050/630)/3)

4= e^(t*ln(1050/630)/3)

Taking ln on both sides

ln 4= t*ln(1050/630)/3

3 ln 4/ ln(1050/630)=t

t=8 yrs approximately