Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has
$3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account?
Compound interest formula: V(t)= P 1-
t = years since initial deposit
n = number of times compounded per year
r= annual interest rate (as a decimal)
P = initial (principal) investment
VO) = value of investment after t years
2 years
9 years
18 years
36 years
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Nexs

18 years

Step-by-step explanation:

Formula:   V(t) = P* (1 +  r/2)^(2t)

r = 4% = 0.04

P =$1,900

V(t) = $1,900 *(1 + 0.04/2)^ (2t)

V = 1900 *(1.02)^(2t)

$3,875.79  =  1900 * 1.02^2t

3875.79/1900 =  1.02^ (2t)

2.0398894736842  = 1.02 ^(2t)

ln 2.0398894736842 =  ln (1.02^(2t) )

ln 2.0398894736842 =  2*t*ln (1.02)

ln 2.0398894736842  /(2* ln (1.02)) =  t

0.71289562682179 / (2 * 0.0198   )  = t

18.00002 years  = t

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

so, converting firstly the mixed fractions to improper fractions and then "adding".