08.11.2022

Sam wants to create a linear function and an exponential function, both of which have a y-intercept of (0,8) and pass through the point (9,512). Help Sam create his functions.

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09.07.2023, solved by verified expert
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Step-by-step explanation:

Exponential function is

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

where a is the y intercept, or the initial value.

b is the constant rate.

Since a is the y intercept, this means a is 8. So we have

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

Now, plug in 9 for x. 512 for y to find b.

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

So the equation is

Sam wants to create a linear function and an, №18010957, 08.11.2022 23:09

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Mathematics
Step-by-step answer
P Answered by Master

Step-by-step explanation:

Exponential function is

y = a \times  {b}^{x}

where a is the y intercept, or the initial value.

b is the constant rate.

Since a is the y intercept, this means a is 8. So we have

y = 8 \times  {b}^{x}

Now, plug in 9 for x. 512 for y to find b.

512 = 8 \times  {b}^{9}

64 =  {b}^{9}

\sqrt[9]{64}  = b

64 {}^{ \frac{1}{9} }  = b

4 {}^{ \frac{1}{3} }  = b

\sqrt[3]{4}  = b

So the equation is

y = 8( \sqrt[3]{4} ) {}^{x}

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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