1.Solve the following system of equations:

Which exponential function goes through the points (1, 16) and (4, 128)?

djyliett [7]

Answer:

Here is the complete question (attachment).

The function which represent the given points are $f(x)=8(2)^{x}$

Step-by-step explanation:

We know that a general exponential function is like, $y=a(b)^{x}$

We can find the answer by hit and trial method by plugging the values of $(x,y)$ coordinates.

Here we are going to solve this with the above general formula.

So as the points are $(1,16)$ then for $x=1,\ y=16$

Can be arranged in terms of the general equation.

$ab^1=16$ ...equation(1) and $ab^4=128$ ...equation(2)

$a\times b=16, then\ a=\frac{16}{a}$

Plugging the values in equation 2.

We have

$\frac{16}{b} b^4=128,16\times b^3=128,b=\sqrt[3]{\frac{128}{16}} =\sqrt[3]{8}=2$

Plugging $b=2$ in equation 1.

We have $a=\frac{16}{b} =\frac{16}{2} =8$

Comparing with the general equation of exponential $a=8$ and $b=2$

So the function which depicts the above points = $y=8(2)^x$

From theoption we have B as the correct answer.

7 0

3 years ago

If two polynomial equations have real solutions, then will the equation that is the result of adding, subtracting, or multiplyin

kirill115 [55]

No. A polynomial equation in one variablel ooks like P(x) = Q(x), where P and Q are polynomials.

Consider polynomial equations x^2 = 3 and x^2 = 1.

Obviously they have real solutions.

Subtract the two polynomial equations:

(x^2 - x^2) = (3 - 1)

0 = 2...

We get the polynomial equation 0 = 2. We call this a polynomial equation because single constants are also by definition polynomials.

Obviously 0 = 2 has no real solution.

3 0

2 years ago

Solve for x and verify:3(x+3)-2(x-1)=5(x-5)

Gekata [30.6K]

Answer:

x=9

Step-by-step explanation:

Distribute:

3x+9-2x+2=5x-25

Combine like terms:

x+11=5x-25

Solve:

x-x+11=5x-x-25

11=4x-25

11+25=4x-25+25

36=4x

Divide by 9:

x=9.

Hope this helps :D

7 0

3 years ago

Read 2 more answers

Question 16 of 50

saul85 [17]

Equation:

y=6,000(1.05)^5

Answer:
7657

8 0

1 year ago

A meteorologist is monitoring the atmospheric pressure as his height above sea level varies. The meteorologist determines that t

Burka [1]

Answer:

The function $p(n)$ is represented by $p(n) = 103\cdot (0.88)^{n}$ .

Step-by-step explanation:

Statement indicates that atmospheric pressure decreases exponentially when height above sea level is increased. This fact is represented by the following model:

$p(n) = p_{o}\cdot r^{n}$ (Eq. 1)

Where:

$p_{o}$ - Atmospheric pressure at sea level, measured in kilopascals.

$r$ -Atmospheric pressure decrease rate, dimensionless.

$n$ - Height above sea level, measured in kilometers.

$p(n)$ - Current pressure, measured in kilopascals.

If we know that $p_{o} = 103\,kPa$ and $r = 0.88$ , the function $p(n)$ is represented by:

$p(n) = 103\cdot (0.88)^{n}$

4 0

3 years ago