Question

At a water park the relationship between C, the total cost of admission, and the number of tickets purchased, is described by the function C = 15t + 2. Which statement is true? 1.An increase of 1 ticket purchased leads to an increase of $2 in total cost 2.An increase of 1 ticket purchased leads to an increase of $15 in total cost. 3.An increase of 1 ticket purchased leads to an increase of $17 in total cost. 4.An increase of 1 ticket purchased leads to an increase of $30 in total cost.

Answer 1

2).An increase of 1 ticket purchased leads to an increase of $15 in total cost.

Explanation

check every option

$C=15t+2$

Step 1

An increase of 1 ticket purchased leads to an increase of $2 in total cost?

Let's check

a) when ticket is 1

t=1

replace,

$\begin{gathered} C=15t+2 \\ C=15\cdot1+2 \\ C=17 \end{gathered}$

now, when t=2( an increase of 1)

$\begin{gathered} C=15t+2 \\ C=15\cdot2+2 \\ C=32 \end{gathered}$

we went from 17 to 32, so the increase in the total cost is not 2, the increase is 15

therefore, the option 1 is not the answer

Step 2

An increase of 1 ticket purchased leads to an increase of $15 in total cost. ?

as we saw in the past point, the increase is 15, , to get the increase

$\begin{gathered} Increase=C(x+1)-C(x) \\ Increase=32-17 \\ Increase=15 \\ \end{gathered}$

so,option 2 is true

Step 3

An increase of 1 ticket purchased leads to an increase of $17 in total cost.?

again, in the previous answer we prove the increase is 15, so

option 3 is not true

Step 4

4.An increase of 1 ticket purchased leads to an increase of $30 in total cost.​?

again, in the previous answer we prove the increase is 15, so

option 4 is not true

I hope this helps you