Question

Mr. Hughes is competing in the Mr. Legs campaign to raise money for the Coral Shores High School scholarship fund. On the first day, he collected $2. On the third day, he collected $8. Let D represent each collection day and N represent the number of dollars collected on that day.
Matt says claims the situation can be modeled by an exponential function. Emily disagrees and claims the number of dollars collected can be modeled by a linear function.

Which statement is true about the number of dollars predicted to be collected on the 6th day based on the two models?


A. The number of dollars predicted to be collected on the 6th day using an exponential model is less than that predicted using a linear model

B. The number of dollars predicted to be collected on the 6th day using an exponential model is greater than that predicted using a linear model

C. The number of predicted to be collected on the 6th day using an exponential model is equal to that predicted using a linear model

D. There is not enough information to determine the relationship between the amount of money predicted to be collected on the 6th day using an exponential model and that predicted using a linear model

Answer 1

The answer is B
2*(2)^6>2(6)+8
128>20

Answer 2

Answer:

Option: B is the correct answer.

B.  The number of dollars predicted to be collected on the 6th day using an exponential model is greater than that predicted using a linear model .

Step-by-step explanation:

Since, on the basis of the given information we can define a exponential function that determine the number of dollars in 't' days by N(t) as:

$N(t)=2^t$

Similarly a linear function can be defined as:

$N(t)=3t-1$

( The equation of a linear function is given by solving the equation with the help of slope-intercept form as:

y=mx+c

we are given two points (1,2) and (3,8) with the help of which we can find the value of m and c and hence get the equation of line

since using (1,2)

we get 2=m+c

similarly using (3,8) we get:

8=3m+c

and solve the two equations using method of elimination ).

Now we have to find which function gives the higher value at t=6.

when t=6

Exponential function:

$N(6)=2^6=64$

and when t=6

Linear function gives:

$N(6)=3\times 6-1\\\\N(6)=18-1\\\\N(6)=17$

Hence, The number of dollars predicted to be collected on the 6th day using an exponential model is greater than that predicted using a linear model .

( since 64>17 )