You have to know that the graph of the arctangent function is a flat S-shaped curve that goes through (0, 0) and has asymptotes at ±π/2. The factor of 2 that multiplies it here expands it vertically so the asymptotes are at ±π. The +3 added to the x causes it to be shifted to the left by 3 units.
wheee
Compute each option
option A: simple interest
simple interest is easy
A=I+P
A=Final amount
I=interest
P=principal (amount initially put in)
and I=PRT
P=principal
R=rate in decimal
T=time in years
so given
P=15000
R=3.2% or 0.032 in deecimal form
T=10
A=I+P
A=PRT+P
A=(15000)(0.032)(10)+15000
A=4800+15000
A=19800
Simple interst pays $19,800 in 10 years
Option B: compound interest
for interest compounded yearly, the formula is
where A=final amount
P=principal
r=rate in decimal form
t=time in years
given
P=15000
r=4.1% or 0.041
t=10
use your calculator
A=22418.0872024
so after 10 years, she will have $22,418.09 in the compounded interest account
in 10 years, the investment in the simple interest account will be worth $19,800 and the investment in the compounded interest account will be worth$22,418.09