The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months? 5433 9766 9765 9006

To solve this problem, we need to use the formula for exponential growth:<br /><br />\[ P(t) = P_0 \times (1 + r)^t \]<br /><br />Where:<br />- \( P(t) \) is the population after time \( t \)<br />- \( P_0 \) is the initial population<br />- \( r \) is the growth rate<br />- \( t \) is the time in months<br /><br />Given:<br />- \( P_0 = 4000 \)<br />- \( r = 0.25 \) (25% growth rate)<br />- \( t = 4 \) months<br /><br />Plugging in the values:<br /><br />\[ P(4) = 4000 \times (1 + 0.25)^4 \]<br />\[ P(4) = 4000 \times (1.25)^4 \]<br /><br />Now, calculate \( (1.25)^4 \):<br /><br />\[ (1.25)^4 = 1.25 \times 1.25 \times 1.25 \times 1.25 \]<br />\[ (1.25)^4 = 2.44140625 \]<br /><br />Then multiply by the initial population:<br /><br />\[ P(4) = 4000 \times 2.44140625 \]<br />\[ P(4) = 9765 \]<br /><br />So, the number of mosquitoes after 4 months will be 9765.<br /><br />The correct answer is:<br />9765