Question

Given four functions, place them in order of their y-intercept, from highest to lowest.
f(x) g(x) h(x) j(x)
the function f of x equals 4 to the x minus 2 power, plus 2 g(x) = 8(20)x Al is monitoring the
decay of a population
of fungi. It is reducing
in half every four weeks.
The population started
at 5.
x j(x)
1 8
2 4
3 2
A. ) g(x), h(x),j(x),f(x)
B. ) h(x), j(x),g(x),f(x)
C.) f(x), g(x),j(x),h(x)
D.) j(x), g(x),h(x),f(x)

Answer 1

We are given
f(x) = (x + 4)^(x - 2) + 2
g(x) = 8 (20)^x
j(x) is the given data

We are asked to arrange the functions according to increasing y-intercept. Simply substitute 0 to x and solve for the y-intercept. Doing this, the answer is
C.) f(x), g(x),j(x),h(x)

Answer 2

The y-intercept of j(x) >y-intercept of g(x) > y-intercept of f(x).

How to calculate the y-intercept?

For y-intercept put x=0 in the given function.

$f(x) = 4^{x-2}$

For y-intercept put x=0 in f(x)

The y-intercept of f(x)= $4^{0-2}$ = 1/16

$g(x) = 8(20)^x$

For y-intercept put x=0 in g(x)

The y-intercept of g(x)= $8(20)^0$=1

Since the decay of the population is exponential in nature, so let us consider:

$j(x) = ab^x$

From the table, j(1) =8,  j(2) =4,  j(3) =2

so, $8=ab$...(1)

$4 =ab^2$.....(2)

$2=ab^3$.....(3)

From (1), (2), and (3)

b=1/2

a =16

So, $j(x) = 16(\frac{1}{2} )^x$

So, y-intercept of j(x) = $16(\frac{1}{2} )^0$=16

The y-intercept of j(x) = 16

The y-intercept of g(x) =1

The y-intercept of f(x) =1/16

Therefore, the y-intercept of j(x) >y-intercept of g(x) > y-intercept of f(x).

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