1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
devlian [24]
2 years ago
6

Write the exponential function y = 22(1.35)' in the form y = aekt.

Mathematics
1 answer:
vesna_86 [32]2 years ago
4 0

Answer:

  • y = 22·e^(0.3001t), growing
  • annual rate: 35%
  • continuous rate: 30.01%

Step-by-step explanation:

When an exponential function is in the form ...

  y = ab^t

the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...

  b = 1 +r

In the alternate form, this can be written ...

  y = a·e^(kt)

Comparing the forms, we see that ...

  b = e^k   ⇒   k = ln(b)

__

<h3>(a)</h3>

  y = 22·1.35^t

  k = ln(1.35) ≈ 0.3001

  y = 22·e^(0.3001t)

The growth factor is greater than 1, so the function is growing.

__

<h3>(b)</h3>

The annual growth rate is ...

  r = 1.35 -1 = 0.35 = 35.00%

__

<h3>(c)</h3>

The continuous growth rate is ...

  k = 0.3001 = 30.01%

You might be interested in
What is science and what are some examples of science 2 paragraphs.​
Alisiya [41]
Science is the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.
6 0
3 years ago
–50 × 4 – (–20) =<br><br> i hate math
Umnica [9.8K]
-180 would be your answeer to your uestion if this helps mark brainleastest please
3 0
2 years ago
Read 2 more answers
Please help me ASAP <br> Please help <br> No links please
lisov135 [29]

Answer:

a is height

b is length

c is width

Step-by-step explanation:

4 0
3 years ago
Which is an equation of the line with a slope of 2 that passes through (3,−5)?
Naya [18.7K]

Answer:

equation of a line= y-y¹=m(x-x¹)

y--5=2(x-3)

y+5=2x-6

y=2x-6+5

y=2x-1

7 0
3 years ago
Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.​
love history [14]

Answer:

x3+y3+z3=k  with k is integer from 1 to 100

solution x=0 , y=0 and z=1 and k= 1

For K= 1 , we have the following solutions (x,y,x) = (1,0,0) ; or (0,1,0) ; or (0,0,1) ,

For k =1 also (9,-8,-6) or (9,-6,-8) or (-8,-6,9) or (-8,9,-6) or (-6,-8,9) or (-6,9,8)

And (-1,1,1) or (1,-1,1)

=>(x+y)3−3x2−3xy2+z3=k

=>(x+y+z)3−3(x+y)2.z−3(x+y).z2=k

=>(x+y+z)3−3(x+y)z[(x+y)−3z]=k

lety=αand z=β

=>x3=−α3−β3+k

For k= 2 we have (x,y,z) = (1,1,0) or (1,0,1) or (0,1,1)

Also for (x,y,z) = (7,-6,-5) or (7,-6,-5) or (-6,-5,7) or (-6,7,-5) or (-5,-6,7) or (-5,7,-6)

For k= 3 we have 1 solution : (x,y,z) = (1,1,1)

For k= 10 , we have the solutions (x,y,z) = (1,1,2) or (1,2,1) or (2,1,1)

For k= 9 we have the solutions (x,y,z) = (1,0,2) or (1,2,0) or (0,1,2) or (0,2,1) or (2,0,1) or (2,1,0)

For k= 8 we have (x,y,z) = ( 0,0,2) or (2,0,0) or (0,2,0)

For k= 17 => (x,y,z) = (1,2,2) or (2,1,2) or ( 2,2,1)

For k = 24 we have (x,y,z) = (2,2,2)

For k= 27 => (x,y,z) = (0,0,3) or (3,0,0) or (0,3,0)

for k= 28 => (x,y,z) = (1,0,3) or (1,3,0) or (1,3,0) or (1,0,3) or (3,0,1) or (3,1,0)

For k=29 => (x,y,z) = (1,1,3) or (1,3,1) or (3,1,1)

For k = 35 we have (x,y,z) = (0,2,3) or (0,3,2) or (3,0,2) or (3,2,0) or 2,0,3) or (2,3,0)

For k =36

we have also solution : x=1,y=2andz=3=>

13+23+33=1+8+27=36 with k= 36 , we have the following

we Have : (x, y,z) = (1, 2, 3) ; (3,2,1); (1,3,2) ; (2,1,3) ; (2,3,1), and (3,1,2)

For k= 43 we have (x,y,z) = (2,2,3) or (2,3,2) or (3,2,2)

For k = 44 we have ( 8,-7,-5) or (8,-5,-7) or (-5,-7,8) or ( -5,8,-7) or (-7,-5,8) or (-7,8,-5)

For k =54 => (x,y,z) = (13,-11,-7) ,

for k = 55 => (x,y,z) = (1,3,3) or (3,1,3) or (3,1,1)

and (x,y,z) = (10,-9,-6) or (10,-6,-9) or ( -6,10,-9) or (-6,-9,10) or (-9,10,-6) or (-9,-6,10)

For k = 62 => (x,y,z) = (3,3,2) or (2,3,3) or (3,2,3)

For k =64 => (x,y,z) = (0,0,4) or (0,4,0) or (4,0,0)

For k= 65 => (x,y,z) = (1,0,4) or (1,4,0) or (0,1,4) or (0,4,1) or (4,1,0) or (4,0,1)

For k= 66 => (x,y,z) = (1,1,4) or (1,4,1) or (4,1,1)

For k = 73 => (x,y,z) = (1,2,4) or (1,4,2) or (2,1,4) or (2,4,1) or (4,1,2) or (4,2,1)

For k= 80=> (x,y,z)= (2,2,4) or (2,4,2) or (4,2,2)

For k = 81 => (x,y,z) = (3,3,3)

For k = 90 => (x,y,z) = (11,-9,-6) or (11,-6,-9) or (-9,11,-6) or (-9,-6,11) or (-6,-9,11) or (-6,11,-9)

k = 99 => (x,y,z) = (4,3,2) or (4,2,3) or (2,3,4) or (2,4,3) or ( 3,2,4 ) or (3,4,2)

(x,y,z) = (5,-3,1) or (5,1,-3) or (-3,5,1) or (-3,1,5) or (1,-3,5) or (1,5,-3)

=> 5^3 + (-3)^3 +1 = 125 -27 +1 = 99 => for k = 99

For K = 92

6^3 + (-5)^3 +1 = 216 -125 +1 = 92

8^3 +(-7)^3

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Helpppppppppppppppppp
    11·1 answer
  • A car is traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 25 minutes ​? In 1 hour
    11·1 answer
  • A square has a length of 2(m+3). What is the perimeter of the square?
    14·2 answers
  • The junior class at Summerfield High School sold a total of 375 tickets for their spring festival. The adult tickets sold for $7
    12·1 answer
  • What is the range of f(x)?<br> {xl-2 {x|-2 {yl-5 {yl-5 sy&lt;-1}
    12·1 answer
  • Use square roots to solve<br> x2 - 10x + 25 = 144
    9·2 answers
  • PLEASE HELP ANSWER THESE
    13·1 answer
  • Joans father is 38 years old today how many days old is he?
    9·1 answer
  • 14. A baby weighed 7 lb 3 oz at birth. Four months later, the baby
    7·1 answer
  • Graph the line. y=-4x+7
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!