Answer:
18. D
19. A
20. the y-intercept is 5000 and it represents the initial amount in the savings account
Step-by-step explanation:
For vertical translation of an exponential function, we can remember the following rules:
If exponential function is given in the form [tex]f(x)=a^x[/tex] where a is a constant, then
1. [tex]f(x)=a^x + b[/tex] is the original shifted b units up, and
2. [tex]f(x)=a^x -b[/tex] is the original shifted b units down
Hence, we can say that to shift the function given in the problem, we will "add a 5" to it.
Thus, [tex]f(x)=4^x +5[/tex] is the correct answer.
19.
THis problem can be solved using the exponential growth equation shown below:
[tex]F=I(1*G)^x[/tex]
Where
F is the future amount (4300 in this case)
I is the initial value/amount (325 given)
G is the Growth Factor ("double", "triple" etc. This case it says double so G = 2)
x is the time period
Putting the known values, we can get the equation as:
[tex]F=I(1*G)^x\\4300=325(1*2)^x\\4300=325(2)^x\\4300=325*2^x[/tex]
A is the correct answer.
20.
y-intercept is the point when x = 0. Let's put it and see what the value is:
[tex]y=5000(0.98)^x\\y=5000(0.98)^0\\y=5000(1)\\y=5000[/tex]
Note: anything to the 0th power is 1
Thus the y-intercept is 5000 and it represents the initial amount in the savings account
