If you added this answer what would it be? 12.35 1.80

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

Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the o

Dmitry_Shevchenko [17]

If the required difference is 600 mi, lets start of counting by 10s and multiplying the current number
800-700 = 100
1600-1400 = 200
2400-2100 = 300
3200-2800 = 400
4000-3500 = 500
4800-4200 = 600
if 60 hours pass, they will be 600 miles away from each other.
counting by 10 each time will help with problems like or similar to this.

7 0

3 years ago

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Helpppppp pleaseeeeeeeeee

77julia77 [94]

Answer:

39.9km a day

Step-by-step explanation:

Add up the four kilometers cycled and you should get 159.6km cycled in total. Divide that number by 4 to get 39.9km as a result. So she's wrong.

7 0

3 years ago

Read 2 more answers