Mathematics, 02.07.2019 20:40 davelopez979

30 points ! an investment in a savings account grows to three times the initial value after t years. if the rate of interest is 5%, compounded continuously, t = (blank) years.

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The formula for a compound growth or decay is given by

A = A₀ × (1+growth rate)ⁿ

Where:
A = The final value after 'n' years
A₀ = The initial value
Growth rate = 5% = 0.05

We know that final value = 3 × Initial value
So that's A = 3A₀
Substitute this expression into the formula, we have
3A₀ = A₀ (1+0.05)ⁿ
3A₀ ÷ A₀ = (1.05)ⁿ
3 = (1.05)ⁿ

from here we can use the trial and error method:

take n = 1, then (1.05)¹ = 1.05
take n = 2, then (1.05)² = 1.1025
take n = 3, then (1.05)³ = 1.16
take n = 5, then (1.05)⁵ = 1.3
take n = 10, then (1.05)¹⁰ = 1.6
take n = 20, then (1.05)²⁰ = 2.7
take n = 30, then (1.05)³⁰ = 4.3 ⇒ too big
take n = 25, then (1.05)²⁵ = 3.4
take n = 24, then (1.05)²⁴ = 3.2
take n = 23, then (1.05)²³ = 3.1
take n = 22, then (1.05)²² = 2.9

so, the number of years it takes for the account to grow three times the initial value after 23 years.

Answer from: Quest

idk

step-by-step explanation:

Answer from: Quest

fabric (square meters) cloaks

7 21

4/3 4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is square meter. now we will multiply by 4 to find fabric needed for 4 cloaks.

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30 points ! an investment in a savings account grows to three times the initial value after t year...

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