All categories

2 years ago

Consider the exponential function

Mathematics

2 answers:

ELEN [110]2 years ago

8 0

Answer:

a) 14,278

Step-by-step explanation:

19000 × 0.96⁷

14277.50208

evablogger [386]2 years ago

7 0

Given:

The given function $f(x)=19,000 \cdot 0.96 ^x$ which models the value of Mark’s car, where x represents the number of years since he purchased the car.

We need to determine the approximate value of Mark's car after 7 years.

Value of the car:

The value of the car after 7 years can be determined by substituting x = 7 in the function $f(x)=19,000 \cdot 0.96 ^x$ , we get;

$f(7)=19,000 \cdot 0.96 ^7$

$f(7)=19,000 \cdot 0.7514474781$

$f(7)=14277.502$

Rounding off to the nearest dollar, we get;

$f(7)=14278$

Thus, the approximate value of Mark's car after 7 years is $14278.

Hence, Option a is the correct answer.

You might be interested in

A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.

3 0

1 year ago

Does the federal government have enough power to carry out its constitutional responsibilities? Explain.

photoshop1234 [79]

Answer:

The federal government's "enumerated powers" are listed in Article I, Section 8 of the Constitution. Among other things, they include: the power to levy taxes, regulate commerce, create federal courts (underneath the Supreme Court), set up and maintain a military, and declare war. It is their job to carry out constitutional responsibilities for society.

Step-by-step explanation:

4 0

2 years ago

What z score separates the top 70% of the normal distribution from the bottom 30%?

melamori03 [73]

Z/70over30................

7 0

2 years ago

3 Ximena draws an X shape in the coordinate plane as shown. Draw the images of

VARVARA [1.3K]

When a shape is rotated, it must be rotated around a point.

See attachment for the image of each rotation.

To do this, the top coordinates of the X shape will be transformed using the appropriate rotation rule; the same rule will then be applied to the other parts of the X shape.

The top coordinates of the X shape are:

$A = (0,0)$