Problem

In one savings account, a principal of $\$ 1000$ …

Problem 27 Easy Difficulty

A principal of $\$ 7000$ is invested at $5 \%$ per annum compounded continuously.
(a) Estimate the doubling time.
(b) Sketch a graph showing how the amount increases with time.

Answer

$\text { a) } 14$

Related Courses

Algebra

Precalculus

Chapter 5

Exponential and Logarithmic Functions

Section 6

Compound Interest

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Video Transcript

All right. So the question of yesterday's were given a principle of $7000 invested at 5% per annum, compound and continuously this question split up into A and B and for a we need to estimate the doubling time and be we need to sketch a graph showing how the amount increases with time. So for a we're going to use the rule of seven. Indeed. So we have our estimated doubling time is equal to 70. Divided by r are in this case is equal to five. So are doubling time is going to be roughly 14. So now for B, we need to write out all our points that are going to be in this, um, in this graph So AT T equals zero, our amount is going to be 7000. AT T equals 14 or amount is gonna double and go up to 14,000. AT T equals 28. Our amount is once again going to double and go up to 28,000. AT T equals 42. Once again, the amount is going to double and go up to 56 1000 and next at 56 account is going to double again, Going to double again, become 112,000. And what the graph should look like here is it should look like along with me, pull up a picture. No or wrong. She was a file here. I only did this in God's most just so you could see a more accurate, um, more accurate representation of how it would look. And it would look like this. As you can see, it increases exponentially. So At T equals 14 Woodridge, which would roughly be around there. It's around 14,000 you see, it's like right there ish 14,000 and you can follow the rest up all the way. But that is what your graphs should look like. It increases exponentially as time goes on and it doubles more.

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