Answer:
5) A
6) C
7) B
8) D
9) D
10) A
11) C
12) C
Step-by-step explanation:
5) The graph of an exponential decay function approaches zero, as the values of x grows bigger and bigger.
From the graph, it is only the first graph the has the end behavior of an exponential decay function.
The correct answer is A) I only
6) The given function is [tex]y=2(3^x)[/tex].
From x=1 to x=3, the grows by a factor of [tex]3^{3-1}=3^2=9[/tex]
From x=5 to x=7, the exponential function grows by a factor of [tex]3^{7-5}=3^{2}=9[/tex]
The correct answer is C.
7) The initial value of the car is $20,000.
Since the car loses 20% of its value every year, it has a multiplicative rate of change of [tex]r=\frac{4}{5}[/tex]
Hence the value will decay exponentially.
The correct answer is B.
8) Let the initial population be [tex]P_0[/tex], then after 210 minutes, [tex]P=2P_0[/tex]
This implies that: [tex]2P_0=P_0e^{210k}[/tex]
[tex]\implies k=\frac{\ln(2)}{210}[/tex]
With initial population is [tex]P_0=8000[/tex], we want to find the population after 630 minutes.
[tex]P=8000e^{\frac{\ln(2)}{210}*630}=64000[/tex]
The correct answer is D
9)
Let the initial population be [tex]P_0[/tex], then after 60 minutes, [tex]P=3P_0[/tex]
This implies that: [tex]3P_0=P_0e^{60k}[/tex]
[tex]\implies k=\frac{\ln(3)}{60}[/tex]
With initial population is [tex]P_0=2000[/tex], we want to find the population after 240 minutes.
[tex]P=2000e^{\frac{\ln(3)}{60}*240}=162000[/tex]
The correct answer is D
10) The initial cost is $40 the unit rate per visit to the Gym is
$2
The total cost y, is given by: [tex]y=2x+40[/tex], where x is the number of visit.
With $90, you substitute y=90 and solve for x.
[tex]2x+40=90[/tex]
[tex]2x=50\\x=25[/tex]
The correct answer is A
11) Let [tex]f(x)=3x+2[/tex], then [tex]f(x+2)=3(x+2)+2=3x+6+2=3x+8[/tex]
[tex]f(a+2)-f(a)=3a+8-(3a+2)=3a+8-3a-2=6[/tex]
Therefore the correct answer is C. [tex]y=3x+2[/tex]
12) Let [tex]f(x)=7(0.5)^x[/tex], then [tex]f(x+2)=7(0.5)^{x+2}[/tex]
This implies that:
[tex]\frac{f(a+2)}{f(a)}=\frac{7(0.5)^{x+2}}{f(7(0.5)^{x}}= \frac{7(0.5)^{x}*0.5^2}{f(7(0.5)^{x}}=\frac{0.5^2}{1}=\frac{1}{4}[/tex]
The correct answer is C
