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3 years ago

If f(1) = 6 and f(n) = f(n − 1) +3, then f(7) = (1) 10 (2) 24 (3) 15 (4) 18

Mathematics

1 answer:

Juliette [100K]3 years ago

3 0

Answer:

Step-by-step explanation:

f(n) = f(n − 1) + 3

if n = 7 => f(7) = f(7-1) + 3 = f(6) + 3

if n = 6 => f(6) = f(6-1) + 3 = f(5) + 3

if n = 5 => f(5) = f(5-1) + 3 = f(4) + 3

if n = 4 => f(4) = f(4-1) + 3 = f(3) + 3

if n = 3 => f(3) = f(3-1) + 3 = f(2) + 3

if n = 2 => f(2) = f(2-1) + 3 = f(1) + 3

if f(1) = 6 then f(2) = 9

f(3) = 12

f(4) = 15

f(5) = 18

f(6) = 21

f(7) = 24

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3 years ago

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Jet001 [13]

Answer:

(A)Decay

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(c)First Term

(d) $f(t)=2000(0.8)^t$

(e)$819.20

Step-by-step explanation:

The exponential function for modelling growth or decay is given as:

$A(t)=A_o(1\pm r)^t$ ,

Where:

Plus indicates growth and minus indicates decay.

$A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period$

For a powerful computer that was purchased for $2000, but loses 20% of its value each year.

(a)Since it loses value, it is a decay.

(b)Multiplier

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(d)The function for this problem is therefore:

$f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t$

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3 years ago

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3 years ago

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Elena L [17]

Answer:

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Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

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<em>Additional comment</em>

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

area = 4.5 +3×4 = 16.5 . . . square units

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2 years ago