19. As part of a cookie recipe, you mix cup of chocolate chips for every 1 cups of
2 answers:
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Solution:
To find the equation of line passing through points A (1, 3) and B (3, 7).
we know that, to derive the equation of a line we first need to calculate the slope of the line. Slope m of a line at points and
is given by -
.
Slope of the line at point A(1,3) and B(3,7)
.
.
.
Equation of a line using a point and a slope ,
The equation of line passing through points A (1, 3) and B (3, 7) :
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
___
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)