6. Find dthe time required for an investment of $10,000 to grow to $18,000 at an annualinterest rate of 6% if the interest is compounded(a) yearly.(b) quarterly.(c) monthly.(d) Continuously.7. An amount P dollars is deposited in a regular bank account. How long does it take todouble the initial investment (called the doubling time) if(a) The interest rate r is compounded annually.(b) The interest rate r is compounded continuously.8. A jealous student started a malicious rumor on an isolated college campus of 5000students. The number of people who know of the rumor within t days after it wasstarted is given by the function5000R(t)1+ ae-kt'Half the students had known of the rumor within ten days.(a) Find a and k.(b) How many students would have known of the rumor within 15 days after itstarted?(c) How many students altogether will know the rumor?9. The burial cloth of an Egyptian mummy is estimated to contain 59% of the carbon-14it contained originally. Use the formula: A(t) = C ()*amount, and h is half-life in years. How long was the mummy buried?where t is years, C is initial

6) Given: P=$10,000, A=$18,000 and r=6%=0.06. The Compound Interest Formula is given by, A=P1+rnnt…

Answered: 6. Find dthe time required for an…

6. Find dthe time required for an investment of $10,000 to grow to $18,000 at an annual interest rate of 6% if the interest is compounded (a) yearly. (b) quarterly. (c) monthly. (d) Continuously.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 40E

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

6. Find dthe time required for an investment of $10,000 to grow to $18,000 at an annual
interest rate of 6% if the interest is compounded
(a) yearly.
(b) quarterly.
(c) monthly.
(d) Continuously.
7. An amount P dollars is deposited in a regular bank account. How long does it take to
double the initial investment (called the doubling time) if
(a) The interest rate r is compounded annually.
(b) The interest rate r is compounded continuously.
8. A jealous student started a malicious rumor on an isolated college campus of 5000
students. The number of people who know of the rumor within t days after it was
started is given by the function
5000
R(t)
1+ ae-kt'
Half the students had known of the rumor within ten days.
(a) Find a and k.
(b) How many students would have known of the rumor within 15 days after it
started?
(c) How many students altogether will know the rumor?
9. The burial cloth of an Egyptian mummy is estimated to contain 59% of the carbon-14
it contained originally. Use the formula: A(t) = C ()*
amount, and h is half-life in years. How long was the mummy buried?
where t is years, C is initial

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