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4 years ago

Convert the exponential function to the form indicated. (Round all coefficients to four significant digits.) f(x) = 2.5 e^(-0.7

x); f(x)=A b^x A = ? b = ?

Mathematics

1 answer:

Jobisdone [24]4 years ago

5 0

$f(x)=2.5e^{-0.7x}=2.5\left(e^{-0.7}\right)^x\\\\A=2.5\\\\b=e^{-0.7}$

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A house worth $70,000 when purchased was worth $67,000 after the first year and $64,000 after the second year. If the economy do

Citrus2011 [14]

Answer:

a) The formula for the sequence is

$a_n = 67,000 -3,000(n-1)$

b) $a_7 = 49,000$

Step-by-step explanation:

Note that the difference between any two consecutive terms in the sequence is always equal to $3,000

$67,000-70,000= -3,000\\\\64,000-67,000=-3,000$

Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.

The explicit formula for an arithmetic sequence is:

$a_n = a_1 +d(n-1)$

Where d is the common difference between the consecutive terms of the sequence

$d = -3,000$

$a_1$ is the first term, or the value of the house after year 1 $a_1= 67,000$

n represents the number of years since the house was purchased

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

a) Then the formula for the sequence is

$a_n = 67,000 -3,000(n-1)$

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

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b) Now we can use the formula to find the price of the house after 7 years

$a_7 = 67,000 -3,000(7-1)$

$a_7 = 67,000 -3,000(6)$

$a_7 = 49,000$

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3 years ago

Among these figures, figure _1._ and figure _2_ have the same volume.

Rom4ik [11]

Answer:

C and D have the same volume

Step-by-step explanation:

For figures such as B, C, and D, with the top area is the same as the bottom area, the volume is the product of the base area and the height. The base area of all these figures is the same, so those (among B, C, and D) with the same height have the same volume.

C and D both have a base area of 20 cm^2 and a height of 5 cm, so both have the same volume.

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For figures such as A and E, with a top area of zero, the volume is 1/3 the product of base area and height. If the heights of A and E were the same, they would have the same volume. The heights are different, so they don't.

None of the figures with non-zero top area have 1/3 the height of either A or E, so none are equal in volume to either of these.

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x = 21/16

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