Answer:
8 years
Step-by-step explanation:
Tim's account balance has an initial value of $6400 and is multiplied yearly by the factor 1.01. Thus, it can be described by the exponential equation ...
b = 6400·1.01^t
where b is the balance after t years.
Putting in the desired balance, we can find t.
6900 = 6400·1.01^t
1.078125 = 1.01^t . . . . . divide by 6400
log(1.078125) = t·log(1.01) . . . . take the logarithm of both sides
log(1.078125)/log(1.01) = t ≈ 7.56 ≈ 8 . . . . . divide by the coefficient of t
It will take Tim approximately 8 years to reach a balance of $6900.
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The problem can also be solved using a graphing calculator.
<em>Complete Question:</em>
<em>The function shown models the depth d (in inches) of snow on the ground during the first 9 hours of a snowstorm, where t is the time (in hours) after the snowstorm begins.
</em>
<em>
The -intercept means that there were[ ]inch(es) of snow on the ground at the start of the storm and the slope means that[ ]inch(es) of snow falls every hour during the storm.
</em>
<em>Function: d(t)= 1/2t+6</em>
Answer:
Step-by-step explanation:
Given
Required
Determine the y intercept and the slope
y-intercept:
A function has a format of:
Where b represent the y intercept:
By comparison of and
Slope:
A function has a format of:
Where m represent the slope
By comparison of and
Answer:
The correct answer is 22.5 in^2
Answer:
y = x⁴ + x³ - 3x² + 5x + C
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Separable differential equations such as these ones can be solved by treating dy/dx as a ratio of differentials. Then move the dx with all the x terms and move the dy with all the y terms. After that, integrate both sides of the equation.
In general (understood that +C portions are still there),
Note that ∫dy = y since it is ∫1·dy = ∫y⁰ dy = y¹/(0+1) = y
For the right-hand side, we use the sum/difference rule for integrals, which says that
![\int \big[f(x) \pm g(x)\big]\, dx = \int f(x)\,dx \pm \int g(x) \, dx](https://tex.z-dn.net/?f=%5Cint%20%5Cbig%5Bf%28x%29%20%5Cpm%20g%28x%29%5Cbig%5D%5C%2C%20dx%20%3D%20%5Cint%20f%28x%29%5C%2Cdx%20%5Cpm%20%5Cint%20g%28x%29%20%5C%2C%20dx)
Applying these concepts:
The answer is y = x⁴ + x³ - 3x² + 5x + C
5:30pm
just add 30 mins to 4:15pm which is 4:45pm then add the 45 mins to that which becomes 5:30pm
