Question

A singer earns $4 million in 2015. During the next 10 years, the earnings increase 7% each year. A. Write an exponential growth model giving the earnings y (in millions of dollars) t years after 2015. Write the base of the model as a decimal. An exponential growth model is y= b. In which year will the player's earnings first exceed $7,000,000?

Answer 1

ninth year

Explanation:

Given the general form of an exponential equation;

P = a(1 +r)^t

We can now write in this particular case;

y = 4 * 10^6(1 + 0.07)^t

The year in which y reaches 7 * 10^6 dollars is

7 * 10^6 = 4 * 10^6 (1 + 0.07)^t

7 * 10^6/4 * 10^6 = (1 + 0.07)^t

1.75 = (1 + 0.07)^t

ln(1.75)= ln(1 + 0.07)^t

ln(1.75) = t ln(1 + 0.07)

0.5596 = 0.06766t

t = 0.5596/0.06766

t = 8 years

So, in the ninth year;

y = 4 * 10^6 (1 + 0.07)^t

y = 4 * 10^6 (1 + 0.07)^9

y = 7.35 * 10^6

Hence, the player's earnings first exceed $7,000,000 in the ninth year.