Question

Question

an annually wet spring has cause the size of the mosquito population in some city by 6%
eache day each day if estamated 210,000 mosqutoes are in the city on may 10th find how
many mosquitoes will inhabit the city on may 27

Answer 1

565,482

Explanation:

As the mosquito population grows by a constant rate of 6% each day, we can use the exponential growth formula to create an equation to find the number of mosquitoes in the city "t" days after May 10th.

Exponential Growth formula

`\boxed{y=a(1+r)^t}`

where:

• y is the number of mosquitoes.
• a is the initial value.
• r is the growth rate (in decimal form.
• t is the time (in days) after May 10th.

Given the size of the mosquito population on May 10th is 210,000:

• a = 210000

Given the growth rate is 6%:

• r = 0.06

Substitute the values of a and r into the formula to create an equation for the number of mosquitos in the city "t" days after May 10th.

`y=210000(1+0.06)^t`

`y=210000(1.06)^t`

To calculate how many mosquitoes will inhabit the city on May 27th, substitute t = 17 into the equation.

`\implies y=210000(1.06)^(17)`

`\implies y=210000(2.69277278...)`

`\implies y=565482.285011...`

`\implies y=565482\; \sf(nearest\;whole\;number)`

Therefore, the number of mosquitoes that will inhabit the city on May 27th is approximately 565,482 to the nearest whole number.