suppose you get a bag of 110 pieces of candy and you decide to eat only 33% of whatever is left in the bag…

Explanation:

Step 1: Choose values for ( d )

We'll choose non - negative integer values for ( d ) (days can't be negative in this context), such as ( d = 0,1,2,3,4 ).

Step 2: Calculate ( c(d) ) for ( d = 0 )

Using the formula ( c(d)=110(0.67)^{d} ), when ( d = 0 ), we know that any non - zero number to the power of 0 is 1. So ( c(0)=110\times(0.67)^{0}=110\times1 = 110 ).

Step 3: Calculate ( c(d) ) for ( d = 1 )

Substitute ( d = 1 ) into the formula: ( c(1)=110\times(0.67)^{1}=110\times0.67 = 73.7\approx74 ) (rounded to the nearest integer).

Step 4: Calculate ( c(d) ) for ( d = 2 )

Substitute ( d = 2 ): ( c(2)=110\times(0.67)^{2}=110\times0.4489 = 49.379\approx49 ) (rounded to the nearest integer).

Step 5: Calculate ( c(d) ) for ( d = 3 )

Substitute ( d = 3 ): ( c(3)=110\times(0.67)^{3}=110\times0.300763 = 33.08393\approx33 ) (rounded to the nearest integer).

Step 6: Calculate ( c(d) ) for ( d = 4 )

Substitute ( d = 4 ): ( c(4)=110\times(0.67)^{4}=110\times0.20151121 = 22.1662331\approx22 ) (rounded to the nearest integer).

To graph the function, we can create a table of values:

( d ) (days)	( c(d) ) (candy left)
0	110
1	74
2	49
3	33
4	22

Then, we plot the points ((0,110)), ((1,74)), ((2,49)), ((3,33)), ((4,22)) on a coordinate plane with the x - axis representing the number of days (( d )) and the y - axis representing the number of candies left (( c(d) )), and draw a smooth curve through these points (since the function is continuous for non - negative real numbers, although we calculated for integer values of ( d )).

Answer:

The table of values for graphing is as follows:

( d )	( c(d) )
0	110
1	74
2	49
3	33
4	22

To graph, plot the points ((0,110)), ((1,74)), ((2,49)), ((3,33)), ((4,22)) and draw a smooth exponential decay curve.