The listing Pagoda of Phan-ling is leaning 5 feet off center . Every 25 years, The pagoda leans an additional foot. It will coll
2 answers:
Answer:
After 125 years pagoda will fell down.
Step-by-step explanation:
The listing pagoda of Phan-ling is leaning 5 feet off center.
The pagoda leans an additional feet every year.
To form the function representing this situation we will use the equation y = mx + c
where c = Initial leaning of pagoda off the center
m = rate of leaning of the pagoda
As given in the statements written above c = 5 feet
and m =
So the function will be f(x) =
This equation represents the whole phenomenon of leaning of pagoda.
We have to find the years remaining in the fall of pagoda if after 10 feet leaning pagoda will collapse.
Now we have to find the value of f(10)
10 =
10 - 5 = 0.04x
x =
x = 125 years
After 125 years pagoda will fall down.
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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
___
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)