random sample has been taken from a normal population and two confidence intervals constructed using exactly the same data. The
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Answer:
Collin: about $401 thousand
Cameron: about $689 thousand
Step-by-step explanation:
A situation in which doubling time is constant is a situation that can be modeled by an exponential function. Here, you're given an exponential function, though you're not told what the variables mean. That function is ...
In this context, P0 is the initial salary, t is years, and d is the doubling time in years. The function gives P(t), the salary after t years. In this problem, the value of t we're concerned with is the difference between age 22 and age 65, that is, 43 years.
In Collin's case, we have ...
P0 = 55,000, t = 43, d = 15
so his salary at retirement is ...
P(43) = $55,000(2^(43/15)) ≈ $401,157.89
In Cameron's case, we have ...
P0 = 35,000, t = 43, d = 10
so his salary at retirement is ...
P(43) = $35,000(2^(43/10)) ≈ $689,440.87
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Sometimes we like to see these equations in a form with "e" as the base of the exponential. That form is ...
If we compare this equation to the one above, we find the growth factors to be ...
2^(t/d) = e^(kt)
Factoring out the exponent of t, we find ...
(2^(1/d))^t = (e^k)^t
That is, ...
2^(1/d) = e^k . . . . . match the bases of the exponential terms
(1/d)ln(2) = k . . . . . take the natural log of both sides
So, in Collin's case, the equation for his salary growth is
k = ln(2)/15 ≈ 0.046210
P(t) = 55,000e^(0.046210t)
and in Cameron's case, ...
k = ln(2)/10 ≈ 0.069315
P(t) = 35,000e^(0.069315t)
So,
Obviously, the car will travel 70 miles in one hour. So after one hour, the car will have traveled 70 miles. That leaves 18 miles.
The time it will take for the car to go another 18 miles will be 18 divided by 70.
Simplify.
Divide.
≈ 0.25714
So a car traveling at 70 mph will take approximately 1.25714 hours or 1.26 hours to travel 88 miles.
Obviously, the car will travel 70 miles in one hour. So after one hour, the car will have traveled 70 miles. That leaves 18 miles.
The time it will take for the car to go another 18 miles will be 18 divided by 70.
Simplify.
Divide.
≈ 0.25714
So a car traveling at 70 mph will take approximately 1.25714 hours or 1.26 hours to travel 88 miles.