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sergij07 [2.7K]
3 years ago
13

Shota invests $2000 in a certificate of deposit that earns 2% in interest each year.Write a function that gives the total v(t) i

n dollars of the investment t years from now
Mathematics
1 answer:
brilliants [131]3 years ago
7 0

Answer:

The correct answer is v(t) = (principal × time × 0.02) if calculated simply and v(t) = Principal × ( 1.02) ^ {time} where v(t) is the interest after t years .

Step-by-step explanation:

Principal amount invested by Shota is $2000.

Interest is earned at 2% per year.

Time for which the principal is invested is t years.

Therefore let the total interest be v(t) dollars in t years.

Case 1: Simple Interest.

v(t) = (principal × time × \frac{r}{100} ) = (2000 × t × 0.02) = 40t

Case 2: Compound Interest.

v(t) = Principal × ( 1+ \frac{r}{100}) ^ {t} - Principal =  2000 × ( 1.02) ^ {t} - 2000.

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Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads
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Answer:

18.87 km/hr

Step-by-step explanation:

First boat is heading North with a speed of 10 km/hr.

Second boat is heading West with a speed of 16 km/hr.

Time for which they move = 2.5 hours

To find:

The speed at which the distance is increasing between the two boats.

Solution:

Let the situation be represented by the attached diagram.

Their initial position is represented by point O from where they move towards point A and point B respectively.

Distance = Speed \times Time

Distance\ OA = 10 \times 2.5 = 25\ km

Distance\ OB = 16 \times 2.5 = 40\ km

We can use Pythagorean Theorem to find the distance AB.

AB is the hypotenuse of the right angled \triangle AOB.

According to Pythagorean theorem:

\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km

The speed at which distance is increasing between the two boats is given as:

\dfrac{47.17}{2.5} \approx 18.87\ km/hr

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