A new popular midsize car has a retail price of $20,000. The midsize car's value M(t) is given by the exponential model M(t) = 20,000(4/5)^t where t represents the time in years. Identify the domain, in yearly intervals, that contains all the years the car's value is less than $1,000. [13, ∞)
[14, ∞)
[15, ∞)
[16, ∞)

[14, ∞)

Step-by-step explanation:

M(t) = 20,000(4/5)^t

Let m(t) > 1000

1000 > 20,000(4/5)^t

Divide each side by 20000

1000/20000 > (4/5)^t

1/20 > (4/5 )^t

Take the log of each side

log (.05) > log(4/5 )^t

Using log a^b = blog a

log (.05) > t log(4/5 )

Divide each side by log (4/5)

log (.05)/ log (4/5) > t

13.42513488>t

Rounding up to the next integer

t = 14