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2 years ago

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3, 576)

Mathematics

1 answer:

sineoko [7]2 years ago

6 0

Answer:

An exponential function in the form y=9(4ˣ)

Step-by-step explanation:

Step(i):-

Given that exponential function

y = a bˣ ...(i)

The equation (i) passes through the point (0,9)

9 = a (b )⁰ = a

a =9

Step(ii):-

The equation (i) passes through the point (3,576)

576 = 9(b)³

⇒ $\frac{576}{9} = b^{3}$

⇒ 64 = b³

⇒ 4³ = b³

$(4^{3} )^{\frac{1}{3} } = (b^{3} )^{\frac{1}{3} }$

b = 4

Final answer:-

An exponential function in the form y=abˣ

An exponential function in the form y=9(4ˣ)

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What is 1 3/4 * 2 1/2

STALIN [3.7K]

Answer:

35/8 or 4.375 in decimal form

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3 years ago

The amount y (in grams) of the radioactive isotope fermium-253 remaining after t hours is y=a(0.5)t/72, where a is the initial a

almond37 [142]

Answer:

Per hour decay of the isotope is 0.96%.

Step-by-step explanation:

Amount of radioactive element remaining after t hours is represented by

$y=a(0.5)^{\frac{t}{72}}$

where a = initial amount

t = duration of decay (in hours)

Amount remaining after 1 hour will be,

$y=a(0.5)^{\frac{1}{72} }$

y = 0.9904a

So amount of decay in one hour = a - 0.9904a

= 0.0096a gms

Percentage decay every hour = $\frac{\text{Amount of decay}}{\text{Initial amount}}\times 100$

= $\frac{0.0096a}{a}\times 100$

= 0.958 %

≈ 0.96 %

Therefore, per hour decay of the radioactive isotope is 0.96%.

7 0

3 years ago

The sum of Sasha’s and Natalie’s ages is 31. Twice Natalie’s age is 11 years more than Sasha’s age. Find each of their ages

ZanzabumX [31]

Answer:

Natalie's age is 14

Sasha's age is 17

Step-by-step explanation:

Let

Sasha's age be "s", and

Natalie's age be "n"

Sum of Sasha and Natalie is 31:

s + n = 31

Twice Natalie is 11 more than Sasha:

2n = s + 11

We ca solve this equation for s first:

s = 2n - 11

We put this into first equation and solve for n first:

s + n = 31

2n - 11 + n = 31

3n = 31 + 11

3n = 42

n = 42/3 = 14

Natalie's age is 14

Also, s = 2n - 11

s = 2(14) - 11

s = 28 - 11

s = 17

Sasha's age is 17

6 0

3 years ago

Eric is a great skateboard fan. He visits a shop named SKATERS to

IceJOKER [234]

Answer:

minimum: 80 zeds

maximum: 137 zeds

Step-by-step explanation:

minimum price is where you choose all the cheapest options

lowest deck price is 40, lowest wheel set price is 14...

40+14+16+10

=40+30+10

=80

maximum price is where you choose all the most expensive options

highest deck is 65, highest price of wheels are 36, hardware 20

65+36+16+20

=65+72

=137

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2 years ago

Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil. What would one pencil and one

vladimir2022 [97]

It is given in the question that

Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil.

Let the cost of pencil is $ x .

Therefore cost of pen is

$$(x+0.40)$

According to the question

$12(x+0.40)+20x =16$

Distributing 12 and combining like terms, we will get

$12x+4.8+20x=16\\32x = 11.2\\x = 0.35$

Therefore cost of pencil is $0.35 and cost of pen is

$0.35+0.40=0.75$

3 0

3 years ago