Ian has a bank account that earns interest. The value, V, in dollars, of Ian's account after T years can be modeled by the exponential function V(t)=5000(1.025)t. Ian claims that the value of his bank account grows by an equal factor each year. To prove his claim, which equation must he show to be true?

a) V(t+1)−V(t)=1.025

b) V(t)−V(t+1)=1.025

c) V(t+1)V(t)=1.025

d) V(t)V(t+1)=1.025

c) V(t+1)V(t)=1.025

Step-by-step explanation:

Data provided in the question

V(t) = 5000 (1.025)^t

The t denotes the time period or the numbe of years

Therefore

We can say that

V(t + 1) = 5000 (1.025)^(t+1)

So it would come like this

= 5000 (1.025)t . (1.025)

hence, we can say that

V(t +1) = V(t) . 1.025

Therefore, the correct option is c.

And hence it is proved by the above calculations

i hope this is what you were looking for.

see attached graph