MATH 1201-01 - AY2024-T2 Written Assignment Unit 5 Using the formula: A=P(1+ r/n)nt
where P is the principal amount, r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the time in years.
For simple interest, the future value (A) is given by: A=P(1+rt)
where r is the annual interest rate (decimal), and t is the time in years.
A(20) = 8500(1 + 0.0812/12)
12*20
A(20) = 8500 (1+ 0006677)
240
= 42922.27
A (20) = 42922.27
Deposit compounded monthly with simple interest:
A(t) = P(1 + r/n*nt)
A(t) = P(1+rt)
A(t) = 8500(1+0.0812*20)
A(t) = 8500*2.624
A(t) = 22304
Thus, there was an exponential increase.
2. Graph the function f(x) = 5(0.5)
-x
and its reflection about the line y = x on the same axis, and give the x – intercept of the reflection. Prove that a
x = e
xlna
a
x = e
xlna
y = 5 *0.5
-x
= 5e
-xln0.5 y/5 = e
-xln0.5
ln(y/5) = -xln0.5 –ln(y/5)/ln0.5 = x y – ln(x/5)/ln0.5
