Help please quick!!!

Nick bought a new car.

ira [324]

Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

In this problem, the car depreciates 12% a year in value, hence r = 0.12 and the equation is given by:

$A(t) = A(0)(0.88)^t$ .

It halves in value at t years, for which A(t) = 0.5A(0), hence:

$A(t) = A(0)(0.88)^t$

$0.5A(0) = A(0)(0.88)^t$

$(0.88)^t = 0.5$

$\log{(0.88)^t} = \log{0.5}$

$t\log{0.88} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.88}}$

t = 5.42.

It takes 5.42 years for the car to halve in value.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

9 0

2 years ago

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

a trail mix has 4 cups of raisins, 3 cups of dates, 6 cups of peanuts, and two cups of cashews. Which ingredients are in the sam

stiv31 [10]

The ratio of dates to peanuts is the same as cashews to raisins. Simplified, both ratios equal 1/2.

8 0

3 years ago

Joshua sells a pack of pens for $3.15, which is 5 percent more than he pays for them. Which equation will help find x, the amoun

nikdorinn [45]

Answer:

x+0.05x=3.15 which has one solution

Step-by-step explanation:

Complete question below:

Joshua sells a pack of pens for 3.15 which is 5 percent more than he pays for them. which equation will help find x, the amount he pays for a pack of pens? how many solutions will this equation have? x+0.05x=3.15, which has infinitely many solutions x+0.5x=3.15, which has one solution x+0.05×=3.15 which has one solution 0.05×=3.15, which has no solution

Let

x= the amount Joshua pays for a pack of pen

5% of x more than he paid for them

=0.05x more

Buying price=0.05x + x

Selling price=3.15

Equate buying and selling price

0.05x + x = 3.15

1.05x=3.15

Divide both sides by 1.05

1.05x / 1.05 = 3.15/1.05

x=3

The equation is 0.05x+x=3.15

The answer is:

x+0.05x=3.15 which has one solution

3 0

3 years ago

A rectangle is 6 meters long and 4 meters wide. What is the area of the rectangle?

ELEN [110]

The answer is 24 cm squared because to find the area of a rectangle you multiply the width by the height. 6 x 4= 24

8 0

1 year ago