Step-by-step answer:
The base of the exponential function is 1.29 for 7 days, as in
f(x) = 86*(1.29)^x
The new rate for days can be calculated by dividing x by 7 (where x remains the number of weeks), namely
f(x) = 86*1.29^(x/7)
Using the law of exponents, b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x
we simplify by putting b=1.29, a=7 to get
f(x) = 86*(1.29^(1/7))^x
f(x) = 86*(1.037)^x since 1.29^(1/7) evaluates to 1.037
Rounding 1.037 to 1.04 we get a (VERY) approximate function
f(x) = 86 * (1.04^x)
1.04 is very approximate because 1.04^7 is supposed to get back 1.29, but it is actually 1.316, while 1.037^7 gives 1.2896, much closer to 1.29.
She was driving an average of 51 mph.
To make this a little easier, you would want to turn 3/4 into 9/12, to match 5/12's denominator.
You would then just add 7/1 to both fractions
(5/12+7/1=12/12 or 1 minutes)
(9/12+7/1=16/12=1 1/3)
So your answer would be 1.333... miles per minute
Hope this helps
See picture below for a geometric view.
Let x = height of building
We use basic trigonometry to find x.
The tangent function = opposite side of right triangle OVER adjacent side of right triangle.
tan(2°) = x/1
Solve for x.
After multiplying both sides by 1 (here 1 represents 1 mile), we get
tan(2°) = x.
We now use the calculator to find x.
In fact, you can take it from here. Use your calculator.