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Answer:
The time it will take the population to grow to 800 insects is 17 days.
Step-by-step explanation:
The growth function of the insects is exponential.
The exponential growth function is:
Here,
<em>y</em> = final value
<em>a</em> = initial value
<em>r</em> = growth rate
<em>t</em> = time taken
It is provided that there were 270 insects after 9 days and initially there were 80 insects.
Compute the value of <em>r</em> as follows:
Now, compute the time it will take the population to grow to 800 insects as follows:
Thus, the time it will take the population to grow to 800 insects is 17 days.
The price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25
<em><u>Solution:</u></em>
Let d" be the price of 1 drink
Let "p" be the price of 1 pretzel
Given that, Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50
<em><u>Therefore, we can frame a equation as,</u></em>
3 x price of 1 drink + 10 x price of 1 pretzel = 54.50
3d + 10p = 54.5 ---------- eqn 1
Jason went into the same movie theater and bought 9 drinks and 5 pretzels, costing a total of $57.25
9 x price of 1 drink + 5 x price of 1 pretzel = 57.25
9d + 5p = 57.25 ---------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
Multiply eqn 1 by 3
9d + 30p = 163.5 ----- eqn 3
<em><u>Subtract eqn 2 from eqn 3</u></em>
9d + 30p = 163.5
9d + 5p = 57.25
( - ) -----------------------
25p = 106.25
p = 4.25
<em><u>Substitute p = 4.25 in eqn 1</u></em>
3d + 10(4.25) = 54.5
3d + 42.5 = 54.5
3d = 54.5 - 42.5
3d = 12
d = 4
Thus price of 1 drink is $ 4 and price of 1 pretzel is $ 4.25