Question

javier bought a painting for $150. each year, the paintings value increases by a factor of 1.15. which expression gives the paintings value after 7 years? choose 1 answer: a $150 + 1.15 cdot 7$ b $(150 + 1.15) cdot 7$ c $150 cdot 1.15^7$ d $(150 cdot 1.15)^7$

Explanation:

Step1: Identify growth type

This is exponential growth, where the value multiplies by 1.15 each year. The general formula for exponential growth is $V = P \cdot r^t$, where $P$ is the initial value, $r$ is the growth factor, and $t$ is time in years.

Step2: Plug in given values

Here, $P = 150$, $r = 1.15$, and $t = 7$. Substitute these into the formula:
$V = 150 \cdot 1.15^7$

Step3: Match with options

This expression matches option C. Options A and B represent linear changes, and option D incorrectly raises the product of initial value and growth factor to the power of 7, which is not the correct exponential growth model.

Answer:

C. $150 \cdot 1.15^7$