a.
To prove: That it takes
a.
Explanation of Solution
Given information: That it takes
Interest rate r compounded continuously.
Formula used: The amount of money in the account after t year is then
Interest paid according to this formula is said to be compounded continuously. The number r is the continuous Interest rate.
Proof:
The amount of money in the account after t year is then
b.
To graph: Graph the functions
b.
Explanation of Solution
Given information: Graph the functions
Graph:
functions
c.
To calculate: Explain why these two rules of thumb for mental computation are reasonable.
c.
Explanation of Solution
Given information: Use the rules to estimate how long it takes to double money at
Formula used: The amount of money in the account after t year is then
Interest paid according to this formula is said to be compounded continuously. The number r is the continuous Interest rate.
Calculation: the functions
d.
To calculate: Use the rules to estimate how long it takes to double money.
d.
Answer to Problem 46E
Money will double in
Explanation of Solution
Given information: Use the rules to estimate how long it takes to double money at
Formula used: The amount of money in the account after t year is then
Interest paid according to this formula is said to be compounded continuously. The number r is the continuous Interest rate.
Calculation: Use the rules to estimate how long it takes to double money at
The amount of money in the account after t year is then
e.
To calculate: Use the rules to estimate how long it takes to triple money.
e.
Answer to Problem 46E
Money will triple in
Explanation of Solution
Given information: Use the rules to estimate how long it takes to triple money.
Formula used: The amount of money in the account after t year is then
Interest paid according to this formula is said to be compounded continuously. The number r is the continuous Interest rate.
Calculation: Use the rules to estimate how long it takes to double money at
The amount of money in the account after t year is then
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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