£40,000 is invested at 8% p.a. If interest is

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 fan has five equally spaced blades. suppose you line up two fans directly on top of each other. What is the least number of de

Irina18 [472]

Answer:

72°

Step-by-step explanation:

There are 5 blades, equally spaced. So the angle between adjacent blades is 360° / 5 = 72°. So you can rotate the fan 72° and the blades will align again.

7 0

3 years ago

{(1, 1), (2, 2), (3, 3), (4,4)} domain and range

jarptica [38.1K]

Answer:

Domain: 1, 2, 3, 4

Range: 1, 2, 3, 4

Step-by-step explanation:

The domain is the first coordinate in an ordered pair which is x. In this set of ordered pairs, the first coordinates ( x ) are 1, 2, 3, 4. The range is the second coordinate in an ordered pair which is y. The range of this set of ordered pairs is 1, 2, 3, 4.

Hope This Helps :)

6 0

2 years ago

Read 2 more answers

Please help asap! 20 points for helping and show all work

Alona [7]

14x2=28
28 divided by 3 is 9.3
the answer is 9.3

6 0

2 years ago

HELP!!! The graph is at the top! Will mark as brainliest answer!!

Alex777 [14]

Answer:

The value of BEF = 36°

Step-by-step explanation:

Given:

Angle AED = 90°

Angle BEF = 3x°

Angle CEF = 54°

Find;

The value of BEF

Computation:

We know that;

Angle AED = Angle BEC (Vertical opposite angle)

So,

Angle AED = Angle Angle BEF + Angle CEF

90 = 3x + 54

3x = 90 - 54

3x = 36

x = 36 / 3

x = 12

The value of BEF = 3x

The value of BEF = 3(12)

The value of BEF = 36°

4 0

2 years ago