Mathematics, 30.06.2019 07:30 jagdeep5533

Ayoung couple purchases their first new home in 2002 for $120,000. they sell it to move into bigger home in 2007 for $150,000. first, we will develop an exponential model for the value of the home. the model will have the form v(t)=v0ekt. let t be years since 2002 and v(t) be the value of the home.

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Answer from: mcadoo774

The exponential model for the value of the home is $V(t)=120000e^{0.045t}$ .

Step-by-step explanation:

According to the give information 2002 is the initial year and the value of the hom in 2002 is $120,000.

The model will have the form

$V(t)=V_0e^{kt}$

Where V₀ is initial value of home, k is a constant and t is number f years after 2002.

$V(t)=120000e^{kt}$

The value of home in 2007 is $150,000. Difference between 2007 and 2002 is 5 years. Therefore the value of function is 150000 at t=5.

$150000=120000e^{k(5)}$

$\frac{150000}{120000}=e^{5k}$

$\frac{5}{4}=e^{5k}$

Take ln both sides.

$ln(\frac{5}{4})=lne^{5k}$

$ln(\frac{5}{4})=5k$ ( lne^a=a )

$\frac{ln(\frac{5}{4})}{5}=k$

$k=0.04462871\approx 0.045$

Therefore exponential model for the value of the home is $V(t)=120000e^{0.045t}$ .

Where t is number of years after 2002.

Answer from: juniorracer148

$V(t)=120000*e^{(0.044)t}$

Step-by-step explanation:

If the given equation is $V(t)=V₀*e^{kt}$ .............(i)

Here from the question it is given that

V(t) = $150,000

V₀=$120,000

t= 2007-2002=5 years

e≅2.718

k=?

Now for the Value of k putting all values in equation (i)

$150000=120000*e^{k(5)}$

$e^{5(k)}=\frac{150000}{120000}$

$e^{5(k)}=\frac{5}{4}$

Now taking Natural log on both sides of the equation

㏑ (e^{5(k)})= ㏑\frac{5}{4}

as we Know that ln(e)=1

5k = 0.223

dividing both sides by 5 gives

k = $\frac{0.223}{5}$

k= 0.044

Now as we got the value of k we can form a general exponential equation which will be

$V(t)=V₀*e^{(0.044)t}$

here value of v₀ is 120000

so equation will be

$V(t)=120000*e^{(0.044)t}$

Answer from: Quest

345

step-by-step explanation:

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

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