Respuesta :
Answer:
(a) [tex]C=1.25\cdot (1.5)^{y/10}[/tex]
(b) $7.44
(c) Yes.
Step-by-step explanation:
The exponential function representing the cost of a movie ticket in a large city is as follows:
[tex]C=1.25\cdot (1.5)^{d}[/tex]
(a)
A decade equals 10 years.
Then for n decades the number of years will be,
y = 10 × n
Then the equation of the cost of a movie ticket in terms of y years after 1953 is as follows:
[tex]C=1.25\cdot (1.5)^{d}[/tex]
[tex]=1.25\cdot (1.5)^{(10\times n)/10}\\=1.25\cdot (1.5)^{y/10}[/tex]
The equation represents the cost of a movie ticket in
(b)
For the year 1953, the value of y is 0.
So, for 1996 the value of y will be, 44.
Compute the cost of a movie ticket in 1996 as follows:
[tex]C=1.25\cdot (1.5)^{y/10}[/tex]
[tex]=1.25\cdot (1.5)^{44/10}\\=1.25\times 5.9539\\=7.442375\\\approx 7.44[/tex]
Thus, the cost of a movie ticket in 1996 will be $7.44.
(c)
It is already provided that the cost of a movie ticket in a large city has increased exponentially over the decades since 1953.
So, for the year 1953 the cost of a movie ticket was, $1.25.
And the cost of a movie ticket in 1996 was $7.44.
This value shows an exponential increase in the cost.
Thus, the estimate in part b is reasonable.
