Which expression shows the results of applying the distributive property to 12(5y+4)

Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

zloy xaker [14]

Answer:

A)

$k=0$

B)

$\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}$

C)

$\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}$

Step-by-step explanation:

We are given the function:

$\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}$

A)

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

$\displaystyle (20) = 20e^{k(1)}$

Simplify:

$1= e^k$

Anything raised to zero (except for zero) is one. Therefore:

$k=0$

B)

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

$\displaystyle (40) = 20e^{k(1)}$

Simplify:

$\displaystyle 2 = e^{k}$

We can take the natural log of both sides:

$\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}$

By definition, ln(e) = 1. Hence:

$\displaystyle k = \ln 2$

Therefore:

$2k+1 = 2\ln 2+ 1 \approx 2.3863$

C)

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

$\displaystyle (10) = 20e^{k(1)}$

Simplfy:

$\displaystyle \frac{1}{2} = e^k$

Take the natural log of both sides:

$\displaystyle \ln \frac{1}{2} = k\ln e$

Therefore:

$\displaystyle k = \ln \frac{1}{2}$

Therefore:

$\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931$

3 0

3 years ago

Stuart paid $ 48.00 for a New tennis racket ,which was 64% of the original price what was the original price of the racket.

Trava [24]

Seventy five dollars hope this could help[

5 0

4 years ago

John has 13 boxes of apples. Each box holds 6 apples. If 7 of the boxes are full, and 6 of the boxes are half full, how many app

TEA [102]

John would have 60 apples!
Hope this helps!!!!! And btw tell John to give me some of them apples lol XD

7 0

3 years ago

Solve. 8 – 3x – x = 12 x =?

poizon [28]

You have to isolate x. First you start off by adding the like terms which is -3x and -x. By adding them you get -4x.

8 - 4x = 12

Then you subtract 8 on both sides since it is positive to isolate x.
-4x = 4

Then you divide -4 by both sides and get x=4/-4

4/-4 is simplified to -1 so the answer is x= -1

3 0

4 years ago

50 PTS

liubo4ka [24]

Answer:

The correct option is B.

Step-by-step explanation:

The amount of money, in dollars, in a savings account after x years is given by $M(x) = 10000(1.03)^{x}$

This above equation represents that $10000 becomes M(x) after x years at a rate of interest 3% compounded in each year.

Therefore, the value in the expression 1.03 represents that there is a 3 percent increase in the savings account each year.

So, the correct option is B. (Answer)

8 0

4 years ago