we are given
[tex]f(x)=10(2)^x[/tex]
now, we can compare it with
[tex]f(x)=a(b)^x[/tex]
we can find b
we get
[tex]b=2[/tex]
now, we are given
How would the graph change if the b value in the equation is decreased but remains greater than 1
Let's take
b=1.8
[tex]f(x)=10(1.8)^x[/tex]
b=1.6
[tex]f(x)=10(1.6)^x[/tex]
b=1.4
[tex]f(x)=10(1.4)^x[/tex]
b=1.2
[tex]f(x)=10(1.2)^x[/tex]
now, we can draw graph
now, we will verify each options
option-A:
we know that all y-value will begin at y=0
because horizontal asymptote is y=0
so, this is FALSE
option-B:
we can see that
curve is moving upward when b decreases for negative value of x
but it is increasing slowly for negative values of x
so, this is FALSE
option-C:
we can see that
curve is moving upward when b decreases for negative value of x
but it is increasing slowly for negative values of x
so, this is TRUE
option-D:
we know that curves are increasing
so, the value of y will keep increasing as x increases
so, this is TRUE
option-E:
we can see that
curve is moving upward when b decreases for negative value of x
but it is increasing slowly for negative values of x
so, this is FALSE
