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elena-14-01-66 [18.8K]

3 years ago

6

Edith needs 65 yards of yarn to knit a baby hat and 580 yards of yarn to knit a baby blanket. A ball of yarn contains 420 feet o

f yarn. How many balls of yarn does Edith need to buy to make the baby hat and baby blanket?

1 answer:

umka2103 [35]3 years ago

3 0

Answer:

5

Step-by-step explanation:

There are 3 feet in a yard, so 420 feet is 420/3 = 140 yards.

The total number of yards Edith needs is ...

65 yd + 580 yd = 645 yd

So, the total number of balls of yarn Edith needs is ...

(645 yd)/(140 yd/ball) ≈ 4.61 balls

Edith needs to buy 5 balls of yarn to make her projects.

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

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Answer:

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Step-by-step explanation:

Given exponential function:

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Solution:

The growth factor of an exponential function in the interval $x=a$ and $x=b$ is given by :

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We can check this by plugging in the given points.

The growth factor between $x=1$ and $x=3$ would be calculated as:

$G=\frac{f(3)}{f(1)}$

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Plugging in values.

$G=\frac{3(5)^3}{3(5)^1}$

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$G=(5)^{2}$

∴ $G=25$

Similarly the growth factor between $x=5$ and $x=7$ would be:

$G=\frac{f(7)}{f(5)}$

$f(7)=3(5)^7$

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Plugging in values.

$G=\frac{3(5)^7}{3(5)^5}$

$G=\frac{(5)^7}{(5)^5}$ (On canceling the common terms)

$G=(5)^{(7-5)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Thus, the growth factor remains the same which is =25.

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