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The amount $A$ accumulated after 1000 dollars is invested for $t$ years at an interest rate of 4$\%$ is modeled by the function $A(t)=1000(1.04)^{t} .$a. Find the amount accumulated after 5 years and 10 years.b. Determine how long it takes for the original investment to triple.

a. $A(10)=1000(1.04)^{10}=1000 \times 1.4802 \approx \$ 1480$b. $\log \left(1.04^{t}\right)=\log 3$$t=\frac{\log 3}{\log 1.04} \approx 28$ years, Hence it would take 28years for the original investment to triple

Calculus 1 / AB

Chapter 1

Functions and Graphs

Section 5

Exponential and Logarithmic Functions

Functions

Limits

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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Hey, it's clear. So when you're in here So the amount a accumulated after $1000 is invested for two years on an interest rate of 4% then it could be used with this equation. So for parquet, we have to find the amount accumulated after five years and 10 years. So for T equals five, we got $1217. We're going to do the same thing for 10. When we got $1480 for a part B. The original investment was $1000 so we have to find the ear when it accumulated to become 3000. So we just plug in 3000. You got one point through four equals. The T equals three. We're gonna take a log of both sides. So we got T equals 28 years for the original investment to trip

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