You have the following formula given in the exercise:
[tex]P\mleft(t\mright)=1500\mleft(1+r\mright)^t[/tex]
Where "r" is the annual growth rate (expressed as a decimal) and "t" is the time in years.
Based on the information given in the exercise, you know that the annual growth rate is 6%.
[tex]r=\frac{6}{100}=0.06[/tex]
Notice that 6% can be expressed as a decimal number by dividing it by 100.
Since the information provided is from 1900 to 1950, you can identify that:
[tex]t=50[/tex]
Now you can substitute values into the formula and evaluate:
[tex]P(50)=1500(1+0.06)^{50}\approx27,631[/tex]
Therefore, the answer is: Option a.
