How long will it take for the balance of an account to double if the savings account earns 0.75% annual interest compounded mont
1 answer:
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(a) Differentiate each of the components to get r'(t). The rule is
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
Answer:
b.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right<u> </u>
<u>Algebra I</u>
- Functions
- Function Notation
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u> </u>
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em /><em />
<em />
<u>Step 2: Differentiate</u>
- Rewrite function [Exponential Rule - Root Rewrite]:
- Chain Rule:
- Basic Power Rule:
- Simplify:
- Rewrite [Exponential Rule - Rewrite]:
<u>Step 3: Evaluate</u>
- Substitute in <em>x</em> [Derivative]:
- Substitute in function values:
- Exponents:
- Multiply:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e