Apainting is purchased for $250. if the value of the painting doubles every 5 years, then its value is given by the function v(t) = 250 • 2t/5, where t is the number of years since it was purchased and v(t) is its value (in dollars) at that time. what is the value of the painting ten years after its purchase? $1,000 $1,400 $1,800 $2,000

Option A is correct.

the value of the painting ten years after its purchase is, $1,000

Step-by-step explanation:

Given the function:

             .....[1]

where,

t is the number of years since it was purchased and

v(t) is its value(in dollars) at that time.

We have to find the value of the painting ten years after its purchase.

⇒ t = 10 years

Substitute in [1] we have;

⇒

⇒

Simplify:

Therefore,  the value of the painting ten years after its purchase is, $1,000

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752