Which situation is best modeled by an exponential function with time as the independent variable? A.
an investment that increases by $30 every year
B.
an investment that takes 2 years to increase in value by $50 and 10 years to increase in value by $250
C.
an investment that increases by $1 every 2 weeks
D.
an investment that increases by a constant factor of 1.03, or at a rate of 3%, every year

there are no short passages to look at

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for