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3 years ago

7

A 40acre field produces 600 bushels of wheat. At the same rate, how many bushels will a 75acre field produce? A) 5 bushels B

) 15 bushels C) 320 bushels D) 1125 bushels

1 answer:

wariber [46]3 years ago

4 0

Since 40 acres of land produces 600 bushels
so the bushels produced by 1 acres of land is 600/40=15
So bushels produced by 75 actes of land = 75×15=1125 bushels

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1 year ago

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3 years ago

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Answer:

a. $y=830*(0.87)^x$

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c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

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Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

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Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be $\frac{830}{2}=415$ .

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Upon dividing both sides of our equation by 830 we will get,

$\frac{415}{830}=\frac{830*(0.87)^x}{830}$

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Let us take natural log of both sides of our equation.

$ln(0.5)=ln(0.87^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

$\frac{-0.6931471805599}{-0.139262067}=x$

$x=4.977286\approx 4.98$

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

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