Answer :
Sure, let's analyze and explain the given statements about the function \( f(t) \), which represents the number of people (in millions) who own cell phones \( t \) years after 1990.
### (a) \( f(10) = 92.7 \)
This statement means that 10 years after 1990, which is the year 2000, 92.7 million people owned cell phones. In other words:
[tex]\[ f(10) = 92.7 \][/tex]
This can be interpreted as:
"The number of people who own cell phones in the year 2000 is 92.7 million."
### (b) \( f(a) = 10 \)
Given \( a = 1 \), this statement means that 1 year after 1990, which is the year 1991, 10 million people owned cell phones. In other words:
[tex]\[ f(1) = 10 \][/tex]
This can be interpreted as:
"The number of people who own cell phones in the year 1991 is 10 million."
### (c) \( f(5) = b \)
Given \( b \) is an unknown variable, this statement means that 5 years after 1990, which is the year 1995, \( b \) million people owned cell phones. In other words:
[tex]\[ f(5) = b \][/tex]
This can be interpreted as:
"\( b \) million people owned cell phones in the year 1995."
### (d) \( f(t) = n \)
Given \( n = 6.2 \), this statement means that \( t \) years after 1990, 6.2 million people owned cell phones. Here, \( t \) is an unknown variable. In other words:
[tex]\[ f(t) = 6.2 \][/tex]
This can be interpreted as:
"6.2 million people own cell phones \( t \) years after 1990."
To summarize:
- (a) The number of people who own cell phones in the year 2000 is 92.7 million.
- (b) The number of people who own cell phones in the year 1991 is 10 million.
- (c) \( b \) million people own cell phones in the year 1995.
- (d) 6.2 million people own cell phones [tex]\( t \)[/tex] years after 1990.
### (a) \( f(10) = 92.7 \)
This statement means that 10 years after 1990, which is the year 2000, 92.7 million people owned cell phones. In other words:
[tex]\[ f(10) = 92.7 \][/tex]
This can be interpreted as:
"The number of people who own cell phones in the year 2000 is 92.7 million."
### (b) \( f(a) = 10 \)
Given \( a = 1 \), this statement means that 1 year after 1990, which is the year 1991, 10 million people owned cell phones. In other words:
[tex]\[ f(1) = 10 \][/tex]
This can be interpreted as:
"The number of people who own cell phones in the year 1991 is 10 million."
### (c) \( f(5) = b \)
Given \( b \) is an unknown variable, this statement means that 5 years after 1990, which is the year 1995, \( b \) million people owned cell phones. In other words:
[tex]\[ f(5) = b \][/tex]
This can be interpreted as:
"\( b \) million people owned cell phones in the year 1995."
### (d) \( f(t) = n \)
Given \( n = 6.2 \), this statement means that \( t \) years after 1990, 6.2 million people owned cell phones. Here, \( t \) is an unknown variable. In other words:
[tex]\[ f(t) = 6.2 \][/tex]
This can be interpreted as:
"6.2 million people own cell phones \( t \) years after 1990."
To summarize:
- (a) The number of people who own cell phones in the year 2000 is 92.7 million.
- (b) The number of people who own cell phones in the year 1991 is 10 million.
- (c) \( b \) million people own cell phones in the year 1995.
- (d) 6.2 million people own cell phones [tex]\( t \)[/tex] years after 1990.
