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andreev551 [17]
3 years ago
5

The points (0,3) and (1,12) are solutions of an exponential function. What is the equation of the exponential function?

Mathematics
1 answer:
AleksandrR [38]3 years ago
6 0

Answer:

A

Step-by-step explanation:

An exponential function has the form

y = a(b)^{x}

Use the given solutions to find a and b

Using (0, 3 ) , then

3 = ab^{0} [ b^{0} = 1 ] , so

a = 3

y = 3(b)^{x}

Using (1, 12 ) , then

12 = 3b^{1} = 3b ( divide both sides by 3 )

4 = b , then

h(x) = 3(4)^{x} → A

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QUESTION
yanalaym [24]

Answer:

$97,958.42

Step-by-step explanation:

To solve this problem we can use the compound interest formula which is shown below:

A=P(1+r )^{t}

<em>P = initial balance </em>

<em>r = interest rate </em>

<em>t = time </em>

<em> </em>

First change 6.5% to its decimal form:

6.5% -> \frac{6.5}{100} -> 0.065

Next plug in the values:

A=49,000(1+.065)^{11}

A=97,958.42

They have to pay back $97,958.42

7 0
3 years ago
A mass of 3.25 kg is attached to the end of a spring that is stretched 22 cm by a force of 15 N. It is set in motion with an ini
mylen [45]

Answer:

Step-by-step explanation:

Given that,

Mass of object=3.25kg

The extension e=22cm=0.22m

Force applied to cause extension F=15N

Initial position Xo=0

Initial velocity Vo=-12m/s

We can get the spring constant from Hooke's law

F=ke

Then, k=F/e

k=15/0.22

k=68.182N/m

Also our natural frequency w is given as

w=√(k/m)

Therefore,

w=√(68.182/3.24)

w=√20.98

w=√21

w=4.58rad/s

w=4.6rad/s

There is no damping in this situation, no outside force acting on the system and the equation that governs the system is

mx''+kx=0

3.25x''+68.182x=0

Divide through by 3.25

x''+20.98x=0

We can approximate 20.98 to 21

x"+21x=0

The solution to this differential equation using D operator

D²+21=0

D²=-21

D= ±√-21

D=±√21 •i

Then the solution is

x(t)=A•Sinwt +B•Coswt

x(t)=A•Sin√21 t +B•Cos√21 t

Note that x'(t)=v(t)

and at t=0 Vo=-12m/s

x(t)=A•Sin√21 t +B•Cos√21 t

x'(t)=v(t)=A√21•Cos√21 t - B√21•Sin√21 t

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

Then, using the two initial conditions

v(0)=-12

And X(0)=0

x(t)=A•Sin√21 t +B•Cos√21 t

X(0)=A•Sin√21•0 +B•Cos√21•0

X(0)=A•Sin0+B•Cos0

0=B

B=0

Also,, V(0)=-12m/s

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

V(0)=A√21•Cos√21•0- B√21•Sin√21•0

V(0)=A√21•Cos0- B√21•Sin0

-12=A√21

Therefore,

A=-12/√21

A=-2.62

Therefore the general equation becomes

x(t)=A•Sin√21 t +B•Cos√21 t

x(t)=-2.62Sin√21 t +0•Cos√21 t

x(t)=-2.62Sin√21 t

a. The amplitude

Comparing x(t) to wave equations

x(t)=-Asin(wt+2λ/t)

Then,

A=2.62m

b. We know the natural frequency already to be

w=√21

w=4.58rad/s

c. Period

Comparing the equation again

wt=√21t

Given that w=2πf

Therefore, 2πft=√21t

Then, f=√21t / 2πt

f=√21/2π

f=0.73Hz

Then, period is the reciprocal of frequency

T=1/f

T=1/0.73

T=1.37seconds

The period is 1.37sec,

5 0
3 years ago
Jayden bought a bike for
alexandr1967 [171]

Answer:

the total cost of the bike including modifying cost is $24,150

Step-by-step explanation:

⇒ bike cost: $21,000

⇒ 15% of $21,000 is 0.15 x 21,000 = 3,150

⇒ initial + additional cost: $21,000 + $3,150 = $24,150

AND WELCOME TO BRAINLY!!

3 0
1 year ago
If there is 10 dollars and someone needs to distribute it to 5 people how much is everyone getting
Kryger [21]
Each person would get 2 dollars
8 0
3 years ago
Read 2 more answers
7 + (10 − 4)2 ÷ 4 × 1\8
natta225 [31]
I’m pretty sure the answer is 12

6 0
3 years ago
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