What is the slope of the line determined by any two solutions to the equation

In exponential growth or decay the increase or decrease is not constant , but it increases or decreases exponentially , i.e. in percentages.

Now let's see the options

a) a palm tree growing 8 inches every year

in this the palm tree is growing at the same constant rate , every year it increases 8 inches only , so this is linear growth.

b) putting $100 in a savings account each week

In this also same as part a , the account is getting $100 , every week , again the growth is linear.

c)a retirement savings account growing by 8% each year

Now in this , the growth is by percentage i.e. let the amount initially was $100 , next year it increases by 8% , and will become 108 , then next year 8% will be calculated on 108 not on 100 , So this growth is exponential

d)a car insurance premium decreasing by $50 each year

here also it is decreasing by $50 each year , decay is constant , not exponential

So answer is OPTION -C