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Natali5045456 [20]
3 years ago
11

Find the exponential function that satisfies the given conditions: Initial value = 31, increasing at a rate of 10% per year

Mathematics
1 answer:
marishachu [46]3 years ago
6 0

Option 2: f(t) = 31.(1.1)^t is the correct answer.

Step-by-step explanation:

Let t be the independent variable time and f(t) be the function that will be used to represent the exponential growth

The general form of an exponential function is given by:

y = a(1+r)^t

Here

a is the initial value of the function while r is the growth rate

and t is the number of years

Given

Initial value = 31

Growth rate = 10% per year

We have to convert the growth rate in decimal

So,

r = \frac{10}{100} = 0.1

Putting the values in the general form

f(t) = 31 . (1+0.1)^t\\f(t) = 31 . (1.1)^t

Hence,

Option 2: f(t) = 31.(1.1)^t is the correct answer.

Keywords: Functions, exponential functions

Learn more about functions at:

  • brainly.com/question/9381523
  • brainly.com/question/9231234

#LearnwithBrainly

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Write an equation of a line in point-slope, slope-intercept, and standard form that has
Inga [223]

Answer:

(a) y + 4x - 14 = 0

(b) y = -4x + 14

(c) y + 4x = 14

Step-by-step explanation:

The formula for calculating the equation of line in point - slope form is given as :

y-y_{1}  = m(x-x_{1} )

where m is the slope

Given from the question :

m = - 4

x_{1} = 2

y_{1} = 6

Substituting into the formula , we have :

y - 6 = - 4(x - 2)

y - 6 = -4x + 8

y + 4x - 6 - 8 = 0

y + 4x - 14 = 0

Therefore :

(a) the equation of the line in point - slope form is y + 4x - 14 = 0

(b) to write it in slope - intercept form , we will make y the subject of the formula , which will give : y = -4x + 14

(c) the equation of line in standard form is ; y + 4x = 14

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3 years ago
What does the whole circle graph represent?
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3 years ago
What is the probability of the following, (for each answer, enter an exact number)
Shalnov [3]

Answer:

Probability of certain event P(E) = 1

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3 years ago
Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84
guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

k = 10/20 and k = 10/20 which are both the same

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Please Help !!!
solong [7]
Best Answer: 2 LiCl = 2 Li + Cl2
mass Li = 56.8 mL x 0.534 g/mL=30.3 g
moles Li = 30.3 g / 6.941 g/mol=4.37
the ratio between Li and LiCl is 2 : 2 ( or 1 : 1)

moles LiCl required = 4.37
mass LiCl = 4.37 mol x 42.394 g/mol=185.3 g


Cu + 2 AgNO3 = Cu/NO3)2 + 2 Ag
the ratio between Cu and AgNO3 is 1 : 2
moles AgNO3 required = 4.2 x 2 = 8.4 : but we have only 6.3 moles of AgNO3 so AgNO3 is the limiting reactant
moles Cu reacted = 6.3 / 2 = 3.15
moles Cu in excess = 4.2 - 3.15 =1.05

N2 + 3 H2 = 2 NH3
moles N2 = 42.5 g / 28.0134 g/mol=1.52
the ratio between N2 and H2 is 1 : 3
moles H2 required = 1.52 x 3 =4.56
actual moles H2 = 10.1 g / 2.016 g/mol= 5.00 so H2 is in excess and N2 is the limiting reactant
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mass NH3 = 3.04 x 17.0337 g/mol=51.8 g
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mass H2 in excess = 0.44 mol x 2.016 g/mol=0.887 g
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4 years ago
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