ACT Exponents and logarithms Practice Questions

The population of a city grows according to the equation $P = 12{,}000 \times 2^{t/10}$, where $P$ is the population and $t$ is time in years. To the nearest whole year, how many years will it take for the population to reach 48,000?

A store initially priced a suit at 40 and then increased its price by a certain percentage each year. After 3 years, the suit's price is 80. Assuming the price increases by the same percentage each year, which equation can be used to find the annual percentage increase?

A store initially priced a suit at 40 and then increased its price by a certain percentage each year. After 3 years, the suit's price is 80. Assuming the price increases by the same percentage each year, which equation can be used to find the annual percentage increase?

A film's box office revenue grows exponentially over time. On its opening day, the film earned $10 million in revenue. After 3 days, the revenue had grown to $135 million. If the revenue continues to grow exponentially at the same rate, how many days after the opening will the revenue first exceed $1 billion?

A new fertilizer increases a crop's yield according to the formula $Y = Y_0 \times 8^{t/3} \times 2^{-t}$, where $Y_0$ is the initial yield and $t$ is time in months. If the initial yield is 10 bushels per acre, what will the yield be after 1.5 months?

A construction company models concrete setting time based on pouring rate. For 15 projects, the natural logarithm of setting time (hours) is plotted against pouring rate (cubic meters per hour). The line of best fit is $\ln(T) = 2.3 - 0.15R$, where $T$ is setting time and $R$ is pouring rate. What is the predicted setting time when the pouring rate is 8 cubic meters per hour?

A new fertilizer increases a crop's yield according to the formula $Y = Y_0 \times 8^{t/3} \times 2^{-t}$, where $Y_0$ is the initial yield and $t$ is time in months. If the initial yield is 10 bushels per acre, what will the yield be after 1.5 months?

A new fertilizer increases a crop's yield according to the formula $Y = Y_0 \times 8^{t/3} \times 2^{-t}$, where $Y_0$ is the initial yield and $t$ is time in months. If the initial yield is 10 bushels per acre, what will the yield be after 1.5 months?