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The linear equation of the tangent at point A is given by:
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
In this problem, to find the slope, we need to find the derivative at (4,3), using implicit differentiation. Hence:
Then:
We use point (4,3) to find b, hence:
Hence, the equation is:
More can be learned about linear equations at brainly.com/question/24808124
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Using compound interest and continuous compounding, it is found that Lincoln would have $15,856 more in his account than Eli.
<h3>What is compound interest?</h3>The amount of money earned, in compound interest, after t years, is given by:
In which:
- A(t) is the amount of money after t years.
- P is the principal(the initial sum of money).
- r is the interest rate(as a decimal value).
- n is the number of times that interest is compounded per year.
Hence, for Lincoln, we have that the parameters are as follows:
P = 49000, r = 0.06125, n = 365, t = 20.
Hence the amount will be of:
The amount is given by:
For Eli, we have that r = 0.05625, hence the amount will be given by:
It is given by:
Lincoln would have $15,856 more in his account than Eli.
More can be learned about compound interest at brainly.com/question/25781328