Mathematics: An initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. about how long has the money been invested? use your calculator and round to the nearest whole number. years

3 equals a3=ab is a times 3b= 3asuba=3b=3(3)b=9...

An initial investment of $100 is now valued at $150.

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09.03.2022

$8\ years$

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$100\\A=\$150\\ r=0.05$

substitute in the formula above

$150=100(e)^{0.05*t}$

$1.5=(e)^{0.05*t}$

Applying ln both sides

ln(1.5)=(0.05t)ln(e)

ln(1.5)=(0.05t)

t=ln(1.5)/(0.05)

$t=8\ years$

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