Assignment - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Math for business

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

Thông tin:

3 trang 6 tháng trước

Tác giả:

Profile Mai Nguyệt
1. If the line, P=(-2/3) Q+6 , is sketched with P on the horizontal axis, and Q on the vertical
axis, which of the following gives the gradient, m, and vertical intercept, c?
-Need to note that if P: Horizontal =>> đổi lại hàm =>>
=>m: -3/2; c: 9
2. During 2020 the price of a good increase by 8%. In the sales on January 1 2021, all items are
st
reduced by 25%. If the sale price of the good is $688.50, find the original price at the beginning of 2020.
If they ask to compute
Percentage need to : increase prevailing 2020
3.
A person wishes to save a regular amount at the beginning of each month in order to buy a
car in 18 months’ time. An account offers a return of 4.8% compounded monthly. Work
out the monthly savings if the total amount saved at the end of 18 months is $18
000. Round your answer to two decimal places.
4. A project requires an initial investment of $7,000, and is guaranteed to yield a return of
$1,500 at the end of the first year, $2,500 at the end of the second year and $x at the end
of the third year. Find the value of x, correct to the nearest $, given that the net present
value (NPV) is $838.18 when the interest rate is 6% compounded annually.
-Initial investment:
-Return: First year = 1500; second = 2500; third year = x$
-
-
5. Supply and demand equations for a certain product are
3Q
S
– 200P + 1800 = 0 =>>
and
3Q
D
+ 100P – 1800 = 0 respectively, where p represents the price per unit in dollars and q
represents the number of units sold per time period. Find the equilibrium price when a tax of
27 cents = $0.27 per unit is imposed on the supplier.
-Equilibrium point: Q = Q
D S
-
- : Imposing tax =>> Supplier will be incurred
Thế vào pt Qd:
=>>
=>>P if tax = $0.27:
6. Find the elasticity for the demand function Q = 80 – 2P – 0.5P averaged along an arc
2
joining P1 = 6 to P2 = 8. Give your answer to two decimal places.
Ta sử dụng midpoint method:
-At
-At 32
=>>
7. The value (in cents) of shares, x years after their flotation on the stock market, is modelled by
V = 6e^0.8x
Find the increase in the value of these shares, to the nearest cent, 4 years and 2 months later.
X: years =>> x = 4 + 2/12=
8. A firm’s average cost function takes the form AC=4Q+a+6/Q and it is known that MC =
35 when Q = 3. Find the value of AC when Q = 6
=>>
MC=35 at Q=3 =>>
=>>
9. A principal of $7,650 is invested at a rate of 3.7% compounded annually. After how many
years will the investment first exceed $12,250? =>> Thế khi nào nó lớn hơn 12250 là được.
10. A firm’s demand function is P = 60 – 0.5Q. If fixed costs are 10 and variable cost are Q +
3 per unit, find the maximum profit
=>> Bấm máy để ra luôn max tại Q=19;
11. Find the sum of the first 12 terms of the geometric series 5 – 20 + 80 – 320 +….
=>> ta có d ng c a sốố h ngạ ủ ạ
Muốốn tính SUM=>>
12. State the degree of homogeneity of the production function
So K by , L by Replacing
We have:
We have:
13.
To compute the real price of houses in 2003:
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1. If the line, P=(-2/3) Q+6 , is sketched with P on the horizontal axis, and Q on the vertical
axis, which of the following gives the gradient, m, and vertical intercept, c?
-Need to note that if P: Horizontal =>> đổi lại hàm =>> =>m: -3/2; c: 9
2. During 2020 the price of a good increase by 8%. In the sales on January 1st 2021, all items are
reduced by 25%. If the sale price of the good is $688.50, find the original price at the beginning of 2020. If they ask to compute
Percentage need to increase prevailing 2020: 3.
A person wishes to save a regular amount at the beginning of each month in order to buy a
car in 18 months’ time. An account offers a return of 4.8% compounded monthly. Work
out the monthly savings if the total amount saved at the end of 18 months is $18
000. Round your answer to two decimal places.
4. A project requires an initial investment of $7,000, and is guaranteed to yield a return of
$1,500 at the end of the first year, $2,500 at the end of the second year and $x at the end
of the third year. Find the value of x, correct to the nearest $, given that the net present
value (NPV) is $838.18 when the interest rate is 6% compounded annually. -Initial investment:
-Return: First year = 1500; second = 2500; third year = x$ - -
5. Supply and demand equations for a certain product are
3QS – 200P + 1800 = 0 =>> and
3QD + 100P – 1800 = 0 respectively, where p represents the price per unit in dollars and q
represents the number of units sold per time period. Find the equilibrium price when a tax of
27 cents = $0.27 per unit is imposed on the supplier. -Equilibrium point: QD = QS - - :
Imposing tax =>> Supplier will be incurred Thế vào pt Qd: =>>
=>>P if tax = $0.27:
6. Find the elasticity for the demand function Q = 80 – 2P – 0.5P2 averaged along an arc
joining P1 = 6 to P2 = 8. Give your answer to two decimal places.
Ta sử dụng midpoint method: -At -At 32 =>>
7. The value (in cents) of shares, x years after their flotation on the stock market, is modelled by V = 6e^0.8x
Find the increase in the value of these shares, to the nearest cent, 4 years and 2 months later.
X: years =>> x = 4 + 2/12=
8. A firm’s average cost function takes the form AC=4Q+a+6/Q and it is known that MC =
35 when Q = 3. Find the value of AC when Q = 6 =>> MC=35 at Q=3 =>> =>>
9. A principal of $7,650 is invested at a rate of 3.7% compounded annually. After how many
years will the investment first exceed $12,250? =>> Thế khi nào nó lớn hơn 12250 là được.
10. A firm’s demand function is P = 60 – 0.5Q. If fixed costs are 10 and variable cost are Q +
3 per unit, find the maximum profit
=>> Bấm máy để ra luôn max tại Q=19;
11. Find the sum of the first 12 terms of the geometric series 5 – 20 + 80 – 320 +…. =>> ta có d ng c ạ a sốố h ủ ng ạ Muốốn tính SUM=>>
12. State the degree of homogeneity of the production function
So Replacing K by , L by We have: We have: 13.
To compute the real price of houses in 2003: