In science class, Victor started an experiment using a solution with a temperature of

4400 dollars is placed in an account with an annual interest rate of 7.5%. To the nearest tenth of a year, how long will it take

Katarina [22]

Answer:

Step-by-step explanation:

The equation for the amount of money in an account after a certain amount is deposited and compounded after t years once per year is

$A(t)=P(1+r)^t$

Our A(t) = 33800, P = 4400, r = .075 and we are looking for t. Filling in:

$33800=4400(1+.075)^t$ and

$33800=4400(1.075)^t$

Begin by dividing both sides by 4400 to get

$7.681818182=1.075^t$

The only way to move that t our from its current position as an exponent is to take the natural log of both sides and follow the rules for natural logs:

$ln(7.6181818182=ln(1.075)^t$

The power rule of natural logs says we can move that exponent down in front, giving us:

$ln(7.681818182)=t*ln(1.075)$

Divide both sides by ln(1.075) to get

$\frac{ln(7.61818182)}{ln(1.075)} =t$

Do this division on your calculator to get

t = 28.2 years

6 0

3 years ago

Read 2 more answers

You reflect triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1), across the x-axis, across the y-axis, and across

notka56 [123]

Answer:

P'( 4, -4)

Step-by-step explanation:

The double reflection across the x-axis does nothing, so the net effect is a single reflection across the y-axis. That effect is to negate the x-coordinate:

reflection across y-axis: (x, y) ⇒ (-x, y)

Then P(-4, -4) ⇒ P'(4, -4)

4 0

3 years ago

Bill has to carry 153 apples from a farm to the market. How many baskets will he need, given that each basket can hold 32 apples

Anon25 [30]

5 baskets (rounded up from 5.78125 and change)

3 0

3 years ago

Let C(t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C(t) decreases at a rate that is pr

tia_tia [17]

Answer:

See explanation below

Step-by-step explanation:

In this case, let's answer this by parts:

<u>a) Concentration at time t when Co is concentration at t = 0:</u>

In this case, we will use the initial expression but without the 2, so:

C(t) = -kC

In this case, we want to know the concentration at time t so:

C'(t) = -kC(t) derivating:

dC/dt = -kC

dC/C = -kdt From here, we can do integrals so:

lnC = -kt + C₁ (1)

Now, it's time to replace t = 0 and C = C₀:

lnC₀ = -k(0) + C₁

lnC₀ = C₁ (2)

Replacing (2) in (1) we have:

lnC = -kt + lnC₀

lnC - lnC₀ = -kt

ln(C/C₀) = -kt

C/C₀ = e^(-kt)

C(t) = C₀ e^(-kt) (3)

This is the expression for C at given time t.

<u>2. time to eliminate 80% of the drug:</u>

With the first data, we need to calculate the value of k, which will be constant at any given time so:

C(t) = C₀ e^(-kt)

0.5C₀ = C₀ e^(-30k)

0.5 = e^(-30k)

ln(0.5) = -30k

k = 0.02310

Now with this value we can calculate the time to eliminate 80% of the drug or simply in other words, that we just have a remaining of 0.2C₀:

0.2C₀ = C₀ e^(-0.0231t)

ln(0.2) = -0.0231t

-ln(0.2) / 0.0231 = t

t = 69.67 h

This is the time to eliminate 80% of the drug

8 0

3 years ago

4

erma4kov [3.2K]

Hello again!

Answer is 60%

————————

so, for this one you first figure out how many study French.

2/9 of 270 is 60 (simple method: 1/9 is 270 divided by 9, which is 30. So 2/9 is 1/9 multiplied by 2, which is 60).
60 are doing French.

Then use this in the ratio of French to Spanish (3:7) and you have 3 and 60 on the same side. You have to multiply 3 by 20 to get to 60 (or divide 60 by 20 to get 3).
So the number you use to do the same to the other side of the ratio is 20.

7 multiplied by 20 (or 7 multiplied by 10, then multiply that by 2) to get 140.
140 are doing Spanish.

Then take the French and Spanish from the big total and you get 270-140-60=70
70 are doing German.

Of these 70, 42 are boys. 70-42 gives 28 girls. 42/70 is the fraction of boys doing German. This is the same as 6/10 and to get a percentage you multiply the fraction by 10 so that the bottom of it is out of 100 (so that’s 60/100).

And 60/100 is the same as 60%.

So your answer is 60%

6 0

3 years ago