Question

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a single tree produces about $2.6 \times 10^4$ pounds of oxygen each year. the amazon rainforest has about $3.9 \times 10^{11}$ trees.
about how many pounds of oxygen are produced in the amazon rainforest per day?
enter your answer by filling in the box.
$2.8 \times 10^{\square}$ pounds per day

Explanation:

Step1: Calculate annual oxygen production

First, find the total oxygen produced per year by all trees. Multiply the oxygen per tree per year ($2.6 \times 10^{4}$) by the number of trees ($3.9 \times 10^{11}$). Using the rule of exponents $a^m \times a^n = a^{m + n}$ and multiplying the coefficients:
$2.6 \times 3.9 \approx 10.14$, and $10^{4} \times 10^{11} = 10^{15}$. So annual production is approximately $10.14 \times 10^{15} = 1.014 \times 10^{16}$ pounds.

Step2: Convert annual to daily production

There are 365 days in a year. Divide the annual production by 365:
$\frac{1.014 \times 10^{16}}{365} \approx 2.778 \times 10^{13}$ (since $\frac{10^{16}}{365} \approx 2.7397 \times 10^{13}$, and $1.014 \times 2.7397 \approx 2.78$).

Step3: Match the given form

The problem states the answer as $2.8 \times 10^{\square}$. From our calculation, $2.8 \times 10^{13}$ fits, so the exponent is 13.

Answer:

13