Question

If the number of apples that grow on a tree per day can be modelled by the equation $y=3^x$, where $x$ is the number of days. There is a container in which the apples are stored and consumed all on the same day. If the capacity of the container is $\mathrm{4,000}$, calculate on which day will the tree produce too many apples for the container to support?

$({\log }_{10}2=0.3,{\log }_{10}3=0.4)$

• A. Day $6$
• B. Day $7$
• C. Day $8$
• D. Day $9$

Answer 1

Answer: (D)

Day $9$

Number of apple on a tree is given by $3^x$ in $x$ days.

A container can hold $4000$ apples in total.

The day when the tree produce too many apples for the container to support is:

$3^x=4000$

Taking $\log$ with base $10$ on both sides , we get

$x\log 3=\log 4000$

$\Rightarrow x\log 3=2\log 2+3\log 10$

$\Rightarrow 0.4x=0.6+3$

$\Rightarrow x=9$

Hence, on day $9$ container is full.