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adell [148]
3 years ago
7

Find the exponential function that satisfies the given conditions:

Mathematics
1 answer:
Nady [450]3 years ago
4 0

Answer:

f(t) = 66·0.995^t

Step-by-step explanation:

You can try t=0 and t=1 in each of the formulas to see which one gives values of 66 and 0.5% less than 66, or 65.67.

The first function has an initial value of 0.5, so is not correct.

The second function gives f(1) = 99, so is not correct.

The third function gives f(1) = 65.67, so is correct.

The fourth function gives f(1) = 66.33, so is not correct.

_____

You can realize that the multiplier will be 0.5% less than 100%, so will be 99.5% = 0.995. This number shows up only in the third selection.

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The equation y= 1/2 x +4 is graphed below.which equation would intersect this line at (4, 6)?
Anton [14]

Answer:

we have the equation y = (1/2)*x + 4.

now, any equation that passes through the point (4, 6) will intersect this line, so if we have an equation f(x), we must see if:

f(4) = 6.

if f(4) = 6, then f(x) intersects the equation y = (1/2)*x + 4 in the point (4, 6).

If we want to construct f(x), an easy example can be:

f(x) = y = k*x.

such that:

6 = k*4

k = 6/4 = 3/2.

then the function

f(x) = y= (3/2)*x intersects the equation  y = (1/2)*x + 4 in the point (4, 6)

5 0
3 years ago
Your free ride to work ends in 14 days. So, maybe you need a car? How much can you afford to spend? Below is what's available at
garri49 [273]

Step-by-step explanation:

Kindly find attached a screenshot of the price list of some cars from motor 1 .com since you did not provide any in the question, and let us assume it is the same as what is available at a dealership near you.

From the list, since you don't have enough money in your account to buy a car, I will say you should get a 2017 Nissan Versa for $11,990

and 25% of  $11,990 is

(25/100)* 11,990

0.25* 11,990

$2997.5

So you can make a down payment of $2997.5

and pay the remainder of $8992.5 later

6 0
3 years ago
Identify horizontal or vertical compression stretch of the function g(x) = 6x
nexus9112 [7]

Answer:

dhjfydhftb7cuvdihcdjxuihy

5 0
3 years ago
Find the coordinates of P ' if D o, 2.4 (x,y) is applied to the triangle below
guajiro [1.7K]

Answer:

The coordinates of P' are (4.8,-4.8).

Step-by-step explanation:

The rule of dilation D_{o,2.4}(x,y) represent the dilation with scale factor 2.4 and center at origin.

If the scale factor of the dilation is k and the center is (0,0), then

(x,y)\rightarrow (kx,ky)

Since the scale factor is 2.4, therefore

(x,y)\rightarrow (2.4x,2.4y)

From the given figure it is noticed that the coordinates of P are (2,-2). The coordinates of P' are

P(2,-2)\rightarrow P'(2.4(2),2.4(-2))

P(2,-2)\rightarrow P'(4.8,-4.8)

Therefore the coordinates of P' are (4.8,-4.8).

3 0
3 years ago
3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d
pychu [463]

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}

Where <em>A</em> is the final amount, <em>P</em> is the initial amount, <em>r</em> is the interest rate, <em>n</em> is the number of times compounded per year, and <em>t</em> is the number of years.

To obtain $4000 after two years, let <em>A</em> = 4000 and<em> t</em> = 2.

Because the account pays 3% interest compounded monthly, <em>r</em> = 0.03 and <em>n</em> = 12.

Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

\displaystyle A = Pe^{rt}

Where <em>e</em> is Euler's number.

Hence, let <em>A</em> = 4000, <em>r</em> = 0.04 and <em>t</em> = 2. Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}

In conclusion, about $3692.47 should be deposited.

8 0
2 years ago
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