The formula for continuous compound interest is a = pert, where a is the amount of money after compounding, p is the original amount invested, r is the annual interest rate expressed as a decimal, and t is the number of years. for which of these functions does t(r) represent the number of years it would take an amount of money to triple if it were compounded continuously at r percent per year? a) t(r) = r ln 3 b) t(r) = ln 3 r c) t(r) = ln r 3 d) t(r) = 3 ln r

Option B.

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

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

Let

x-------> the Principal amount of money to be invested

we have  

substitute in the formula above  and solve fot t

Applying ln both sides

Convert to function notation

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,