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3 years ago

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one year ago, Charlie's chameleon was 8.42 inches long. Now his chameleon is 9.36 inches long. a.how much did Charlie's chameleo

n grow in the last year. b.how much more does his chameleon need to grow to be exactly 10 inches

2 answers:

Delicious77 [7]3 years ago

3 0

The chameleon grew .94 inches, and would need to grow .64 inches to be exactly 10 inches.

babymother [125]3 years ago

3 0

This is easy, Answer to A is 0.91 because 9.36-8.45=0.91

Answer to B is 0.64 because 10.00 (add the decimal to the end to make it easier to subtract) 10.00-9.36=0.64 (use 9.36 because its his hight now)

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The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

<em>The linear equation of the function is: </em> $g(P) = 22.9P+7$ <em>.</em>
<em>The inverse function is: </em> $g^{-1}(c) = \frac{1}{22.9}(c - 7)$ <em> .</em>
<em>A practical domain is from 0% to 100%</em>
<em>A practical range is from 7 to 29.9 </em>

<u>A. Input quantity</u>

The input quantity is the percentage of frozen citrus crop

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<u>B. Output quantity </u>

The output quantity is the cost of box of oranges

<u>C. The linear function</u>

We have:

$(P_1,c_1) = (20\%,11.58)\\(P_2,c_2) = (80\%,25.32)$

<em>Calculate the slope of the function</em>

$m = \frac{c_2 - c_1}{P_2 - P_1}$

$m = \frac{25.32 - 11.58}{80\%-20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

<em>The linear equation is calculated as follows:</em>

$c -c_1 = m(P-P_1)$

$c -11.58= 22.9(P-20\%)$

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<u>D. Rewrite as y = mx + b</u>

We have:

$c-11.58 = 22.9P-4.58$

Collect like terms

$c = 22.9P - 4.58 + 11.58$

$c = 22.9P+7$

<em>The function is:</em>

$g(P) = 22.9P+7$

<u>E. A practical domain</u>

The domain is the possible values of P. Because P is a percentage, its possible values are 0% to 100%.

The domain of the function is: $[0\%,100\%]$

<u>F. A practical range</u>

When P = 0%

$c = 22.9 \times 0\% + 7 = 7$

When P = 100%

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

G. The meaning of $g^{-1}(12)$

The inverse function of g(P) is $g^{-1}(P)$

So:

$g^{-1}(12)$ is the percentage of frozen citrus crop, when the cost is $12.

<u>H. The inverse formula</u>

We have:

$c = 22.9P+7$

Subtract 7 from both sides

$c - 7 = 22.9P$

Make P the subject

$P = \frac{1}{22.9}(c - 7)$

So, the inverse formula is:

$g^{-1}(c) = \frac{1}{22.9}(c - 7)$

Substitute 12 for c

$g^{-1}(12) = \frac{1}{22.9}(12 - 7)$

$g^{-1}(12) = \frac{1}{22.9} \times 5$

$g^{-1}(12) = 22\%$

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