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2 years ago

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

Mathematics

2 answers:

Liono4ka [1.6K]2 years ago

8 0

Answer:

optian 2

Step-by-step explanation:

Trava [24]2 years ago

4 0

f (n + 1) = f(n) – 5 is the recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1

<h3><u>Solution:</u></h3>

Given that,

f(1) = 6 and n ≥ 1

Given sequence is 6, 1, -4, -9, -14

<em><u>Let us first analyse the logic used in this sequence</u></em>

6 - 5 = 1

1 - 5 = -4

-4 - 5 = -9

-9 - 5 = -14

Thus the next terms in sequence are obtained by subtracting 5 from previous term

Thus a recursive formula can be formed as:

f (n + 1) = f(n) – 5

Where "n" is the nth term

Let us check our recursive formula:

f(1+ 1) = f(1) - 5

f(2) = f(1) - 5

f(2) = 6 - 5 = 1

Thus we have got f(2) = 1 which is correct as per given sequence

You might be interested in

World wind energy generating1 capacity, W , was 371 gigawatts by the end of 2014 and has been increasing at a continuous rate of

Sunny_sXe [5.5K]

Answer:

a) $W(t) = 371(1.168)^{t}$

b) Wind capacity will pass 600 gigawatts during the year 2018

Step-by-step explanation:

The world wind energy generating capacity can be modeled by the following function

$W(t) = W(0)(1+r)^{t}$

In which W(t) is the wind energy generating capacity in t years after 2014, W(0) is the capacity in 2014 and r is the growth rate, as a decimal.

371 gigawatts by the end of 2014 and has been increasing at a continuous rate of approximately 16.8%.

This means that

$W(0) = 371, r = 0.168$

(a) Give a formula for W , in gigawatts, as a function of time, t , in years since the end of 2014 . W= gigawatts

$W(t) = W(0)(1+r)^{t}$

$W(t) = 371(1+0.168)^{t}$

$W(t) = 371(1.168)^{t}$

(b) When is wind capacity predicted to pass 600 gigawatts? Wind capacity will pass 600 gigawatts during the year?

This is t years after the end of 2014, in which t found when W(t) = 600. So

$W(t) = 371(1.168)^{t}$

$600 = 371(1.168)^{t}$

$(1.168)^{t} = \frac{600}{371}$

$(1.168)^{t} = 1.61725$

We have that:

$\log{a^{t}} = t\log{a}$

So we apply log to both sides of the equality

$\log{(1.168)^{t}} = \log{1.61725}$

$t\log{1.168} = 0.2088$

$0.0674t = 0.2088$

$t = \frac{0.2088}{0.0674}$

$t = 3.1$

It will happen 3.1 years after the end of 2014, so during the year of 2018.

7 0

1 year ago

The following table shows the number of hours some teachers in two schools expect students to spend on homework each week: Schoo

Lerok [7]

Answer:

For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5

For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5

No, the box plots are not symmetric.

Step-by-step explanation:

Part A

The given data sets are

School A : 9,14,15,17,17,7,15,6,6

School B : 12,8,13,11,19,15,16,5,8

Arrange the data in ascending order.

School A : 6,6,7,9,14,15,15,17,17

School B : 5,8,8,11,12,13,15,16,19

Divide each data set in four equal parts.

School A : (6,6),(7,9),14,(15,15),(17,17)

School B : (5,8),(8,11),12,(13,15),(16,19)

For school A:

Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17

Interquartile range of the data is

$IQR=Q_3-Q_1=16-6.5=9.5$

For school B:

Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19

Interquartile range of the data is

$IQR=Q_3-Q_1=15.5-8=7.5$

Part B:

The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data set are different.

4 0

2 years ago

At the beginning of the business day, a bank's vault held $575,900. By the end of the day, $(3.5 103) had been added to the vaul

Likurg_2 [28]

3.5*10^3=3,500

3,500+ 575,900=579,400

5 0

2 years ago

15,000 blue trout were released into the Meherrin River for a scientific study. The function, f(x) = 15,000 (98)x , represents t

Norma-Jean [14]

Answer:

I'm guessing you mean f(x)=15,000(9/8)^x. If this is what you mean, the population would increase by about 12,000 (12030.4870605 to be exact).

Step-by-step explanation:

Starting equation: f(x)=15,000(9/8)^x

You can clean up the 9/8 to be 1.125

Now what you want to do is find the answer to (9/8)^5 which is 1.8020324707

Next multiply 1.8020324707 by 15,000 and you get 27030.4870605

Finally 27,030.4870605 - 15,000 gives you 12030.4870605. Which means that the population increased by about 12,000.

0 0

2 years ago

Pooja's plant began sprouting 2days before Pooja bought it, and she had it for 98 days until it died. At its tallest, the plant

taurus [48]

Given that function H(t) models the height of Pooja's plant (in centimeters) where t is the number of days after she bought it.

Now we have to find about which number type is more appropriate for the domain of h. That means what values can be taken by the variable "t".

Since t is number of days not the hours so t will not use decimal or fraction values. It can use integer values for the number of days.

Since time is counted after she bought the plant then number of days will be positive.

Hence answer for the type of domain can be positive integers or you can say integers greater than or equal to 0.

4 0

2 years ago

Read 2 more answers