Question

An unusually wet spring has caused the size of a mosquito population in some city to increase by 66​% each day. If an estimated 2424​0,000 mosquitoes are in the city on May 77​, find how many mosquitoes will inhabit the city on May 2323. Use yequals=2424​0,000left parenthesis 1.06 right parenthesis Superscript x(1.06)x where x is number of days since May 77.
Question content area bottom
Part 1
On May 2323 there will be approximately enter your response here mosquitoes.
​(Round to the nearest thousand as​ needed.)

Answer 1

The given formula for the mosquito population \( y \) is:

\[
y = 24240000 \left(1.66\right)^x
\]

where \( x \) is the number of days since May 7.

First, we need to calculate how many days are between May 7 and May 23:

From May 7 to May 23 is:

\[
23 - 7 = 16 \text{ days}
\]

Now substitute \( x = 16 \) into the formula:

\[
y = 24240000 \left(1.66\right)^{16}
\]

Now we need to calculate \( (1.66)^{16} \):

\[
(1.66)^{16} \approx 79.3060 \quad \text{(using a calculator)}
\]

Now substitute this value back into the equation:

\[
y \approx 24240000 \times 79.3060
\]

Calculating this gives:

\[
y \approx 1922557440
\]

Now rounding this to the nearest thousand:

\[
y \approx 1922560000
\]

So, the estimated number of mosquitoes in the city on May 23 is approximately:

\[
\boxed{1922560000}
\]