The amount of money invested in a certain account increases according to the following function, where is the initial amount of the investment, and is the amount present at time (in years).

y= yoe^0.035t

After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answer to the nearest tenth.

The number of years it would take the initial investment to double is 19.8 years.

The formula used to calculate the value of an investment after a specified number of years with continuously compounded interest is:

FV =  A x x N

y = x t

y /   = 2

log(2) ÷ log(e) ÷ 0.035

= 19.8 years

A similar question was answered here: link

Therefore the initial amount will be doubled after 19.8 years.

Step-by-step explanation:

Given that,

The amount of money increases according to the following function

where = the initial amount of the investment, and y = the amount present at time t (in years).

Let after t years the initial amount will be double.

, t=t

Taking ln both sides

                [ ]

years

Therefore the initial amount will be doubled after 19.8 years.

answer: the common difference is -0.10