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Molodets [167]
3 years ago
8

Stanley Bank offers a money market account that earns 1.85% compounded continuously: a) If $10,000 is invested in this type of a

ccount, how much will it be worth in 3 years? b) How long will it take for the account to be worth $15,000?
Mathematics
1 answer:
Alexxx [7]3 years ago
5 0

Answer:

a) $1056.33 b) 23 years

Step-by-step explanation:

a) 10000(1+1.85/100)^3=10565.33 (2d.p.)

b) let x be the no. of years

15000 = 10000(1+1.85/100)^x

1.5 = 1.0185^x

ln both sides

ln 1.5 = x ln 1.0185

x = ln 1.5/ln 1.0185

=22.11

=23 years (rounded up)

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3 years ago
a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and
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The time taken for the upward motion is 1 second. The same time is taken for the downward motion

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Step-by-step explanation:

The equation of motion is:

x(t) = -4.9t^{2} + 9.8t

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format x(t) = at^{2} + bt + c

The vertex is the point (t_{v}, x(t_{v})), in which

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In this question:

x(t) = -4.9t^{2} + 9.8t

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It reaches a maximum height of 4.9 meters.

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From the vertex to the ground.

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It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

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