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monitta
3 years ago
8

For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.

Mathematics
1 answer:
Zolol [24]3 years ago
8 0

Answer:

Step-by-step explanation:

Expression that defines a growth function is,

f(x)=a(1+r)^t

Here, a= initial amount

r= growth rate

And (1+r) = Growth factor

Similarly, decay function is represented by the expression,

f(x)=a(1-r)^t

That means if a function has a growth factor (1 + r) or greater than 1, function will have a exponential growth.

And a function with growth factor between 0 to 1, it will be a decay.

1). f(t)=1.18^t

  f(t)=(1+\frac{18}{100})^t

  Growth rate = 18%

  Here, 1.18 > 1

  Therefore, function is a growth function.

2). g(t)=2^{-2t}

    g(t)=(2^{-2})^t

    g(t)=(\frac{1}{2})^t

    g(t)=(0.5)^t

    g(t)=(1-\frac{50}{100})^t

    Decay rate = 50%

    Here growth factor (0.5) is less than 1.

    Therefore, function is a decay function.

3). h(t)=1.19^\frac{t}{10}

    h(t)=(1.19^{\frac{1}{10}})^t

           =1.017^t

           =(1+0.017)^t

           =(1+\frac{1.7}{100})^t

     Growth rate = 1.7%

     Growth factor (1.19) is greater than 1.

     Therefore, function will be a growth function.

4). k(t)=0.13^t

           =(1-0.87)^t

           =(1-\frac{87}{100})^t

    Decay rate = 87%

    Growth factor (0.13) < 1

    Therefore, function will be a decay function.

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Kim is 5 years older than her brother Jack. If the sum of their ages is 21, find each of their ages.
yarga [219]

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Answer:

  • Kim is 13
  • Jack is 8

Step-by-step explanation:

Let k represent Kim's age. Then Jack's age is k-5 and the total of their ages is ...

  k + (k -5) = 21

  2k = 26 . . . . . . . add 5, collect terms

  k = 13 . . . . . . . . . divide by 2; Kim's age

  k -5 = 8 . . . . . . . Jack's age

Kim is 13; Jack is 8.

7 0
3 years ago
How do you write 70% as a fraction in simplest form ?
alexdok [17]
70% equals to 70/100 in fraction form.
But, you need to write it in simplest form. so, divide both of them from 10 'cause they both can divide completely by it.
70/100 = 7/10
so, your answer is 7/10
3 0
4 years ago
Please!!! Help!!! Brainliest of Right! it goes as 50 point in the end but i used 100 point if you help me i will help you!!
vekshin1

Answer:

2.  3.913 kg (3 dp)

3.  light cream

4.  240 CoffeeStops

5.  7 CoffeeStops per square mile

6.  2,861 cups of coffee each day

Step-by-step explanation:

Given:

  • Skim milk density at 20 °C = 1.033 kg/l
  • Light cream density at 20 °C = 1.012 kg/l
  • 1 liter = 0.264 gallons

<u>Question 2</u>

\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}

Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)

---------------------------------------------------------------------------------------------

<u>Question 3</u>

Given:

  • Volume of liquid = 9 liters
  • Mass of liquid = 9.108 kg

\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}

Therefore, the container holds light cream.

---------------------------------------------------------------------------------------------

<u>Question 4</u>

Given:

  • 15 CoffeeStops per 100,000 people
  • Population of Manhattan ≈ 1,602,000 people

\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}

Therefore, there are 240 CoffeeStops.

---------------------------------------------------------------------------------------------

<u>Question 5</u>

Given

  • Manhattan ≈ 34 square miles

\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}

Therefore, the density of CoffeeStops is 7 per square mile.

---------------------------------------------------------------------------------------------

<u>Question 6</u>

Given:

  • Each person buys 3 cups of coffee per week

\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}

\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}

Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.

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3 years ago
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nalin [4]
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6 0
3 years ago
If 4C + 3 = 15, what is the value of C?
Soloha48 [4]
4c+3=15
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So you minus it from each side so you
4c=12
12/4=3
So c =3
4 0
3 years ago
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