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shtirl [24]
2 years ago
6

Sophia expects the number of cows, C C, on her farm t t years from now to be modeled by the function C ( t ) = 3 0 ( 2 ) C(t)=30

(2) t . Additionally, she expects the supply of hay, F F, in tons, that her crops can provide for each cow t t years from now to be modeled by the function F ( t ) = 8 ( 1 . 5 ) F(t)=8(1.5) t . Let H H be the total yearly amount of hay produced in Sophia's farm (in tons) t t years from now. Note that the hay produced on Sophia's farm is used exclusively to feed her cows. Write the formula of H ( t ) H(t) in terms of C ( t ) C(t) and F ( t ) F(t).
Mathematics
1 answer:
topjm [15]2 years ago
8 0

Answer:

The expression is given as:

H(t)=C(t)\times F(t)=240\times 3^t.

Step-by-step explanation:

Sophia expects the number of cows, C, on her farm t years from now to be modeled by the function:

C( t ) = 30\times (2)^t

Additionally, she expects the supply of hay, F, in tons, that her crops can provide for each cow t years from now to be modeled by the function

F( t ) =8\times (1.5)^t

Let H be the total yearly amount of hay produced in Sophia's farm (in tons) t years from now.

Total amount of Hay produced in sophia's farm= Number of cows in farm×Amount of hay required for each cow.

i.e. H(t)=C(t)×F(t)

H(t)=30\times 8\times (2)^t\times (1.5)^t

and we know that a^x\times b^x=(a\times b)^x=(ab)^x

Hence,H(t)=240\times (2\times 1.5)^t\\\\H(t)=240\times 3^t.

Hence, the hay produced on Sophia's farm is used exclusively to feed her cows i.e. we need to write the formula of H ( t ) in terms of C(t) and F (t) is:

H(t)=C(t)\times F(t)=240\times 3^t.


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Answer:

The distance to his office is 2.5 miles.

Step-by-step explanation:

Given : Wade bicycles at a speed of 10 miles an hour and arrives at his office in only 15 minutes.

To find : What is the distance in miles to his office?

Solution :

The relationship between distance, speed and time is

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The speed of bicycle is 10 miles per hour.

Time taken is 15 minutes.

Converting into hours,

1 hour = 60 minutes

1 minute = \frac{1}{60} hours

15 minute = \frac{15}{60} hours

15 minute = 0.25 hours

Substitute the value sin the formula,

\text{Distnace}=10\times0.25

\text{Distnace}=2.5

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4 0
2 years ago
Michael has a weekly food budget of $62. If he plans to budget the same amount for each of the 7 days of the week, what is the m
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2 years ago
A piggy bank contains some dimes and nickels. There are 8 more dimes than nickels in the bank. There is a total of $1.40. How ma
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4 nickels

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Dimes are worth .1 each while nickels are .05 each.

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If all our nickels and dimes together are worth 1.4 then we have another equation .1d+.05n=1.4

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Because of the known similarity of the triangles, we know that

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A model spaceship costs $15.99 before tax. The tax on the model spaceship is 8%. What is the total cost of the model spaceship?
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