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kobusy [5.1K]
3 years ago
10

What is the exact time t, in years, needed for the balance of an account that earns 5% annual 8. Interest compounded continuousl

y to triple?
Mathematics
1 answer:
Brums [2.3K]3 years ago
3 0

Answer:

It takes 22.52 years for the balance to triple in value.

Step-by-step explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:

A(t) = A(0)(1+r)^t

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that r = 0.05, and thus:

A(t) = A(0)(1+r)^t

A(t) = A(0)(1+0.05)^t

A(t) = A(0)(1.05)^t

Time for the balance to triple?

This is t for which A(t) = 3A(0). So

A(t) = A(0)(1.05)^t

3A(0) = A(0)(1.05)^t

(1.05)^t = 3

\log{(1.05)^t} = \log{3}

t\log{1.05} = \log{3}

t = \frac{\log{3}}{\log{1.05}}

t =  22.52

It takes 22.52 years for the balance to triple in value.

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A​ chef's specialty calls for ​one- fiftieth of an ounce of a spice per serving. The chef has a digital scale that shows the wei
Anna35 [415]

Answer:

The scale reading that the chef need to see for this spice when preparing the specialty for 43 people is 0.86.

Step-by-step explanation:

In order to find the answer, you need to multiply the amount that the chef uses per serving for the number of servings. The statement indicates that the chef uses ​one- fiftieth of an ounce of a spice per serving and this is represented as 1/50 and you have to multiply this for 43 that is the number of people.

You can find 1/50 as a decimal dividing 1 by 50:

1/50=0.02

Now, you can multiply this value for 43:

0.02=43=0.86

According to this, the answer is that the scale reading that the chef need to see for this spice when preparing the specialty for 43 people is 0.86.

3 0
2 years ago
Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloo
blsea [12.9K]

Answer:

He can purchase 300 white baloons.

Step-by-step explanation:

150$ is 15000 cents

15000 = 60b + 30w

b being number of blue baloons,w number of white baloons and 60 and 30 prices in cents

15000 = 60*100 + 30w

15000 - 60*100 = 30w

15000- 6000 = 30w

30w = 9000

w =300

number of white baloons is 300

3 0
3 years ago
Read 2 more answers
A distribution has the five-number summary shown below. What is the range of this distribution? 24, 36, 42, 57, 65
inn [45]
Hello!

To find the range of the distribution, we must order the data from least to greatest (it has already been done) and then subtract the smallest value from the largest value in the set.

In this set, the smallest value is 24, and the largest value is 65. Subtract:

65 - 24 = 41

A N S W E R:

The range of the distribution below is A. 41.
Have a wonderful day!
5 0
3 years ago
Read 2 more answers
The sum of three numbers is 10. Two times the second number minus the first number is equal to 12.
eimsori [14]

<u>Answer:</u>

-10,1,19

<u>Step-by-step explanation:</u>

<u></u>

x+y+z = 10 (Equation 1)

2y-x= 12  (Equation 2)

x-y+2z = 7 (Equation 3)

(Equation 2): -x = -2y+12

                       x = 2y-12 (Equation 4)

(Equation 1) - (Equation 3): 2y-z = 3

                                              -z = -2y+3

                                               z = 2y-3 (Equation 5)

Substitute (4) and (5) into (1)

x+y+z = 10

(2y-12)+y+(2y-3) = 10

5y-15 = 10

5y = 5

y=1

Substitute y=1 into (2)

2y-x= 12

2(1)-x= 12

2-x= 12

-x= 12-2

-x= 10

x= -10

Substitute y=1 and x=-10 into (1)

x+y+z = 10

-10+1+z = 10

z-9 = 10

z = 10+9

z = 19

Order: x = -10, y = 1, and z = 19

8 0
3 years ago
Read 2 more answers
Question 5 and 6 please help me
sp2606 [1]

Problem 5

The function is continuous for the given domain x \ge 6

This is because y = (-5/6)x+5 is itself continuous, and any interval subset of this function is also continuous. We can plug in any real number that is equal to 6 or larger, and get some y output. If we plugged in x = 6, then we'd get

y = (-5/6)x+5

y = (-5/6)*6 + 5

y = -5+5

y = 0

This is the largest y value possible. Why? Because y = (-5/6)x+5 has a negative slope, so the graph is going downhill as you read it from left to right. As x gets bigger, y gets smaller. The smallest x value allowed in the domain produces the largest y value in the range. There is no smallest y value as the y values keep going down forever.

The range is therefore y \le 0

In interval notation, you can write the range as (-\infty, 0]. The square bracket indicates "include this endpoint as part of the range".

======================================================

Problem 6

The function is discrete for this given domain. The domain itself is a discrete list of values. We cannot plug in values between say 0 and 2. We can only substitute one of those values from the list given. Consequently, the y values will also be a list, and not an interval like problem 5 had.

-----------

If you plugged in x = -4, then you should get...

y = (-1/2)*(-4)+2

y = 2+2

y = 4

So the input x = -4 lead the output y = 4

Repeat for x = -2

y = (-1/2)x+2

y = (-1/2)*(-2)+2

y = 1+2

y = 3

and the same for x = 0 as well

y = (-1/2)x+2

y = (-1/2)*0 + 2

y = 0 + 2

y = 2

and x = 2 also

y = (-1/2)x+2

y = (-1/2)*2 + 2

y = -1+2

y = 1

Finally, plug in x = 4

y = (-1/2)x+2

y = (-1/2)*4+2

y = -2+2

y = 0

---------------

If we plugged each of these x values {-4, -2, 0, 2, 4} one at a time into the equation y = (-1/2)x+2, then we get this list of values {4, 3, 2, 1, 0}

Sorting the values from smallest to largest, we have this range {0, 1, 2, 3, 4}

3 0
2 years ago
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