Question

d) approximately how many hours would it take for the population to reach 500 000 cells? 3a

1. an antique painting is purchased in 1995 for $1995. the value increases by 3.25% every year.

a) write an equation that models the value of the painting after t years. 2a
b) determine the increase in value of the painting in the 6th year after it was purchased (from year 5 to year 6). 4t&i

Explanation:

Step1: Write the compound - growth formula

The formula for compound - growth is $V = V_0(1 + r)^t$, where $V_0$ is the initial value, $r$ is the rate of growth as a decimal, and $t$ is the number of time - periods. Given $V_0=1995$, $r = 0.0325$. The equation for the value of the painting after $t$ years is $V(t)=1995(1 + 0.0325)^t=1995(1.0325)^t$.

Step2: Find the value of the painting in the 5th and 6th years

For $t = 5$, $V(5)=1995\times(1.0325)^5$.

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For $t = 6$, $V(6)=1995\times(1.0325)^6$.

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Step3: Calculate the increase in value

The increase in value from year 5 to year 6 is $V(6)-V(5)$.
$V(6)-V(5)\approx2414.52 - 2330.69=83.83$

Answer:

a) $V(t)=1995(1.0325)^t$
b) Approximately $\$83.83$