Which of the following can be modeled with a linear function? Select all that apply. The cost per visit to a community pool. The neighborhood charges a yearly fee to use the pool. The cost to attend a show at the local theatre. Tickets are $12 each. An endangered species population is decreasing by 15% each year. The distance a bicyclist travels when cycling at a constant speed of 30 mph. The population of a town grows at a constant rate each year.

Solution:

Given, the cost of local theatre ticket = $12 each

The endangered species population is decreasing by 15% each year.

Speed of bicyclist = 30 mph.

We have to find the linear function

a) we have to find the cost per visit to a community pool.

Let x be the number of visits to the pool

Let a be the fixed cost of the visit.

Cost per visit to the pool, y = ax

Therefore, the linear function that represents the cost per visit to a community pool is y = ax.

b) the neighborhood charges a yearly fee to use the pool.

Let x be the number of years

Let a be the fixed fee to use the pool.

Yearly fee to use to the pool, y = ax

Therefore, the linear function that represents the yearly fee to use the pool is y = ax.

c) the cost to attend a show at the local theatre. Tickets are $12 each.

Let x be the number of shows

The cost of one show is $12

Cost of x shows is y = 12x

Therefore, the linear function that represents the cost to attend a show at the local theatre is y = 12x.

d) the endangered species population is decreasing at 15% each year.

Let a be the initial population of the species

Let x be the number of years

Decrease rate = 15%

The decrease in the population is given by,

y = a(1 - 0.15)^x

y = a(0.85)^x

Therefore, the above relation does not represent a linear function. It is an exponential function.

e) the distance a bicyclist travels when cycling at a constant speed of 30mph.

Let x be the time

The speed of the cyclist = 30 mph

Distance = speed × time

Distance = 30x

Therefore, the above relation represents a linear function.

f) the population of a town growing at a constant rate each year.

Let a be the initial population of the species

Let x be the number of years

Let r be the constant increase rate per year.

The increase in the population is given by

y = a(1 + r)^x. It is an exponential function.

Therefore, the above relation does not represent a linear function.

Therefore,

a) The cost per visit to a community pool is y = ax

b) The neighborhood charges a yearly fee to use the pool is y = ax

c) The cost to attend a show at the local theatre. Tickets are $12 each. The function is y = 12x

d) An endangered species population is decreasing by 15% each year. y = a(0.85)^x is not a linear function.

e) The distance a bicyclist travels when cycling at a constant speed of 30 mph is y = 30x.

f) The population of a town growing at a constant rate each year is y = a(1 + r)^x is not a linear function.

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Which of the following can be modeled with a linear function? Select all that apply. The cost per visit to a community pool. The neighborhood charges a yearly fee to use the pool. The cost to attend a show at the local theatre. Tickets are $12 each. An endangered species population is decreasing by 15% each year. The distance a bicyclist travels when cycling at a constant speed of 30 mph. The population of a town grows at a constant rate each year.

Summary:

The following can be modeled with a linear function

a) The cost per visit to a community pool is y = ax
b) The neighborhood charges a yearly fee to use the pool is y = ax
c) The cost to attend a show at the local theatre. Tickets are $12 each. The function is y = 12x
d) An endangered species population is decreasing by 15% each year. y = a(0.85)^x is not a linear function.
e) The distance a bicyclist travels when cycling at a constant speed of 30 mph is y = 30x.
f) The population of a town growing at a constant rate each year is y = a(1 + r)^x is not a linear function.