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A sum of $\$ 5000$ is invested at an interest rate of $9 \%$ per year, compounded continuously.a. Find the value $A(t)$ of the investment after $t$ years.b. Draw a graph of $A(t)$.c. Use the graph of $A(t)$ to determine when this investment will amount to $\$ 25,000$.

(a) $A(t)=5000 e^{0.09 t}$(b)(c) After 17.88 years

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

The Natural Exponential Function

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McMaster University

University of Michigan - Ann Arbor

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and the question we are given. But the principal amount equals $5000. The raid off interest is 9% compounded continuously. When David by the value off 80 after years, that's gonna be B E T. That's 5000 times evenings, 2.9 B for part, Bigger us to craft on use that year 84 calculator to craft our function. That's 3000 e days too. Point Do you know mine? B But we use exit for exactly that independent variable recent does window so that we can see the craft Clearly this is on a brooks. You will know that. Yes, there definitely is on Ah, information. So this is what we get. This is the graph that's required and for party here us to find the time at which the amount as $25,000. So we go back to the ground end of I do equals ready 3000 and find the intersection point. So the go through the car window and select intersect option. Find the intersection between these two curved and get it a 17 point in a to 643 We make a note that digs 17.88 years for this amount

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