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LUCKY_DIMON [66]
3 years ago
6

How do you write a function of t that represents the situation(sales $10,000 increase by 65% each year)?

Mathematics
1 answer:
Shkiper50 [21]3 years ago
7 0

Answer:

  s(t) = 10000·1.65^t

Step-by-step explanation:

The general form of an exponential model is ...

  f(t) = (initial value) × (1 +(fractional change))^t

where the fractional change can be positive or negative and t is the number of time units. Each time unit will correspond to the period required for the fractional change.*

__

For your problem, you have (initial value) = 10,000 and (fractional change) = 65% = 0.65 with time units of 1 year. Your function for sales (s) will then be ...

  s(t) = 10000·1.65^t

_____

* The business regarding time units has to do with problems where you get a description like "increased 30% in 4 hours." Then, if t is in hours, the multiplier of the initial value looks like 1.30^(t/4).

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The government of the Republic of Lemon Island plans to transform their lemon-based economy into a tourism-based economy. They d
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Step-by-step explanation:

dy/dt = (A − Be^(-t/5)) y

(a) First, find the general solution by separating the variables and integrating.

dy / y = (A − Be^(-t/5)) dt

dy / y = [A + 5B (-⅕ e^(-t/5))] dt

ln |y| = At + 5B e^(-t/5) + C

y = e^(At + 5B e^(-t/5) + C)

y = Ce^(At + 5B e^(-t/5))

Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:

40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))

40×10⁶ = Ce^(0.2)

C = 40×10⁶ e^(-0.2)

y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))

y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))

(b) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:

50×10⁶ = Ce^(0.02(0) + 0)

50×10⁶ = C

y = 50×10⁶ e^(0.02t)

Comparing to the answer from part (a):

40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)

e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4

-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)

-5 + t + 5e^(-t/5) = 25 ln(5/4)

t + 5e^(-t/5) = 5 + 25 ln(5/4)

Solve with a calculator:

t = 9.886

The transformed economy surpasses the untransformed economy in the 10th year.

(c) In year t=5, the size of the transformed economy is:

y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))

y = 47.6×10⁶

The percent growth is:

(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%

The growth rate is greater than 4%, so the current government can expect to be reelected.

3 0
3 years ago
I alipou
Norma-Jean [14]

Answer:

After the sales tax

$235

before sales tax

210.32

Step-by-step explanation:

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136-51=85. so the common factors would be 1 and 17
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Answer: you don't insult someone when they are being nice to you i i cant even do that c:

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Answer: three dimensional figure and plane.

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