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3 years ago

Find the 8th term of 27,36,48

Mathematics

1 answer:

Sonbull [250]3 years ago

4 0

Step-by-step explanation:

the sequence is a geometric sequence

simply use the formula:

t(n) = a * (r)^n-1

where n = 8, a = 27, r = 4/3

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Determine what type of model best fits the given situation:

lyudmila [28]

Let value intially be = P

Then it is decreased by 20 %.

So 20% of P = $\frac{20}{100} \times P = 0.2P$

So after 1 year value is decreased by 0.2P

so value after 1 year will be = P - 0.2P (as its decreased so we will subtract 0.2P from original value P) = 0.8P-------------------------------------(1)

Similarly for 2nd year, this value 0.8P will again be decreased by 20 %

so 20% of 0.8P = $\frac{20}{100} \times 0.8P = (0.2)(0.8P)$

So after 2 years value is decreased by (0.2)(0.8P)

so value after 2 years will be = 0.8P - 0.2(0.8P)

taking 0.8P common out we get 0.8P(1-0.2)

= 0.8P(0.8)

$=P(0.8)^{2}$ -------------------------(2)

Similarly after 3 years, this value $P(0.8)^{2}$ will again be decreased by 20 %

so 20% of $P(0.8)^{2} \frac{20}{100} \times P(0.8)^{2} = (0.2)P(0.8)^{2}$

So after 3 years value is decreased by $(0.2)P(0.8)^{2}$

so value after 3 years will be = $P(0.8)^{2} - (0.2)P(0.8)^{2}$

taking $P(0.8)^{2}$ common out we get $P(0.8)^{2}(1-0.2)$

$P(0.8)^{2}(0.8)$

$P(0.8)^{3}$ -----------------------(3)

so from (1), (2), (3) we can see the following pattern

value after 1 year is P(0.8) or $P(0.8)^{1}$

value after 2 years is $P(0.8)^{2}$

value after 3 years is $P(0.8)^{3}$

so value after x years will be $P(0.8)^{x}$ ( whatever is the year, that is raised to power on 0.8)

So function is best described by exponential model

$y = P(0.8)^{x}$ where y is the value after x years

so thats the final answer

3 0

3 years ago

A can of peas weighs 10 oz. Explain how you would make a graph to model the total weight of peas in terms of the number of cans

Vika [28.1K]

Ur x axis will be the number of cans and ur y axis will be the weight in oz

u will label ur x axis( the number of cans) in intervals of 1......from 0 to 4
u will label ur y axis (the weight) in intervals of 10....from 0 to 40

ur equation would be : y = 10x
points on this line are : (0,0), (1,10), (2,20), (3,30), (4,40)

3 0

2 years ago

Read 2 more answers

Solve the variable<br> -10+ s/1.5= -5

patriot [66]

Answer:

s = 15 over 2 (15/2 fraction) or 7.5

3 0

2 years ago

Prime factor tree of 385

timama [110]

11*5*7